{"id":37516,"date":"2025-10-14T00:00:34","date_gmt":"2025-10-14T07:00:34","guid":{"rendered":"https:\/\/community.nrs.com\/duct-tape\/?p=37516"},"modified":"2025-10-24T10:33:41","modified_gmt":"2025-10-24T17:33:41","slug":"the-math-equation-that-saved-us_2","status":"publish","type":"post","link":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/","title":{"rendered":"The Math Equation That Saved Us"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">I tried all my tricks. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">I leaned my ear in close while opening and closing the valve: no sound. I hovered the lighter\u2019s flame near the brass attachments: no flame. I unscrewed each attachment and checked the tines weren\u2019t bent. I re-screwed tightly, making sure not to <\/span><i><span style=\"font-weight: 400;\">over<\/span><\/i><span style=\"font-weight: 400;\">screw. I checked the threads for sand and, seeing none, blew on them anyway. <\/span><span style=\"font-weight: 400;\">At this point, I had maxed out my stove repair skills, so in a Hail Mary approximation, I whispered \u201cPlease work,\u201d eight times in a row. I tried again to light the stove. It did not light.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This was night one on the Lower Owyhee. Perhaps the sunbrella and beach emoticon Casey labeled the pre-trip group chat with was misleading. Perhaps it was just optimistic. It was May, after all. Casey and Mika were excited to introduce two coworkers to their first-ever river trip. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">So far, it was not panning out as advertised. The unfavorable conditions included a wind advisory and a rainstorm. Gale-force winds whipped water violently off whitecaps. The upstream gusts were comically unceasing. Rogue waves as big as ocean swells peppered the first eight miles of flatwater. I tried to ignore the swelling blister on my palm.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-37521\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114410\/DTD_Math_JWilhelm_3x2_2-1000x667.jpg\" alt=\"\" width=\"970\" height=\"647\" srcset=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114410\/DTD_Math_JWilhelm_3x2_2-1000x667.jpg 1000w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114410\/DTD_Math_JWilhelm_3x2_2-300x200.jpg 300w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114410\/DTD_Math_JWilhelm_3x2_2-768x512.jpg 768w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114410\/DTD_Math_JWilhelm_3x2_2-1536x1024.jpg 1536w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114410\/DTD_Math_JWilhelm_3x2_2.jpg 1800w\" sizes=\"auto, (max-width: 970px) 100vw, 970px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">The Owyhee Canyonlands are a place that have never, not once, been normal for me. This piece of public land is wild, remote, and wonderfully fickle. When I recreate there, something almost always goes wrong. Our gazetteer doesn\u2019t match Google Maps, and neither map\u2014digital or paper\u2014matches the actual roads.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Once, we got high-centered in a mud puddle. We spent three hours up to our armpits digging ourselves out, all to the soundtrack of pooping cows. Another time, in the same area, at the same time of year, we got high-centered on snow. There have been times I am so hot it feels dangerous to leave my full-body submersion. But then again, at the same time of year, we had to pour boiling water on our frozen shoes just to loosen the laces enough to slip our feet inside. Both high and low water conditions have thwarted expeditions. The Owyhee Canyonlands have bested me more than once, but I love them even more for it.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">If the conditions are right, the Lower Owyhee River is actually a relatively accessible stretch through an otherwise remote and undeveloped area. Usually, the toughest part is the Birch Creek Take Out road, which can wash out with heavy rains. (I avoid thinking about one particular drive out). If there\u2019s rain in the forecast, some people opt to take out at Leslie Gulch instead. Depending on how full the reservoir is, this option involves about 13 miles of deadwater. You can bring your own motor, or hire a tow. On this particular trip, the Birch Creek road was reportedly in rough shape. We booked our shuttle to Leslie when Mika procured a propane-powered motor for us to borrow.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Mika, Casey and I wanted to make sure that Zach and Marie had a good time on their first river trip. When we arrived late at camp after only managing to row nine out of our scheduled 17 miles that day, I went into overdrive.<\/span><\/p>\n<div id='gallery-1' class='gallery galleryid-37516 gallery-columns-3 gallery-size-thumbnail'><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_3x2_6\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114429\/DTD_Math_JWilhelm_3x2_6-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_2x3_2\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114511\/DTD_Math_JWilhelm_2x3_2-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure>\n\t\t<\/div>\n\n<p><span style=\"font-weight: 400;\">\u201cI got kitchen. I\u2019ll boil some water for hot drinks.\u201d I shooed my partner, Casey, towards one of his shivering friends, knowing he\u2019d help with tent setup and extra warm layers as needed. We had <\/span><i><span style=\"font-weight: 400;\">clawed<\/span><\/i><span style=\"font-weight: 400;\"> our way through those nine miles. It was cold, it was wet, it was windy, still. I was trying not to think about making up miles; I just wanted to get everyone\u2019s spirits up with some hot cocoa.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Still clad in my dry suit and PFD, I did five squats, blew air into my cupped hands, and opened the dry box. I hung the dish rack, set up the handwashing station and attached the stove hose to the propane tank. I filled a pot with water.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">That&#8217;s when the stove failed me.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cUmmm,\u201d eyes wide, slightly panicked, I grabbed Casey\u2019s arm as he walked by the kitchen. \u201cI can\u2019t get the stove to work.\u201d I traded his armful of firewood for my lighter and headed to the firepan. Mika joined Casey in the kitchen. With the methodical and precise motions of two ICU nurses, they diagnosed the issue: the propane valve was broken.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cI just got this tank! It\u2019s brand new,\u201d Mika lamented.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cReally?\u201d I asked, eyeing the faded and torn label.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cI mean, I exchanged my empty for a full one, right before the trip,\u201d she said, with incredulity.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-37524 aligncenter\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5.jpg\" alt=\"\" width=\"1800\" height=\"1200\" srcset=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5.jpg 1800w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5-300x200.jpg 300w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5-1000x667.jpg 1000w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5-768x512.jpg 768w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5-1536x1024.jpg 1536w\" sizes=\"auto, (max-width: 1800px) 100vw, 1800px\" \/>\u201cIt\u2019s fine! It\u2019s fine,\u201d I pepped. I started running through our list of meals and mentally planning small adjustments. \u201cWe\u2019ve got a firepan, we\u2019ve got a dutch oven. We can make this work!\u201d<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Mika leveled me with a gaze; \u201cThe motor,\u201d she said gravely.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cThe motor,\u201d I repeated, the implication dawning on me. We had 59 miles to go and two and a half days to do it. Which would have been fine, except we had to be at the take-out early (night nurses need naps before work). And 13 miles of that would have exactly zero downstream current. As if to reiterate the dire nature of the situation, the wind made a gallant surge, flipping two camp chairs and teetering the table dangerously.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cOkay, okay,\u201d I grasped for a positive spin while Mika and Casey did some quick math. We needed to row 34 miles the next day. Oh. Did I mention the water level was hovering just below 1,000 CFS? Biting back my groan, I glared at the propane tank.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cWait. What\u2019s that say?\u201d I indicated words in faded black Sharpie. <\/span><i><span style=\"font-weight: 400;\">Bad val<\/span><\/i><span style=\"font-weight: 400;\"> was just legible. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Mika barked out a laugh. \u201cWell, we rowed all day into incessant wind, but at least our propane tank has a <\/span><i><span style=\"font-weight: 400;\">bad val<\/span><\/i><span style=\"font-weight: 400;\">.\u201d<\/span><\/p>\n<div id='gallery-2' class='gallery galleryid-37516 gallery-columns-3 gallery-size-thumbnail'><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_3x2_3\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114415\/DTD_Math_JWilhelm_3x2_3-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_2x3_1\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114506\/DTD_Math_JWilhelm_2x3_1-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure>\n\t\t<\/div>\n\n<p><span style=\"font-weight: 400;\">My English teachers lectured me not to use double negatives, but the math teachers may have had it right this time. For some reason, two negatives just added up to a positive.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cOur propane tank doesn\u2019t work, but at least our firewood is wet,\u201d Zach added.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cIt took us seven hours to row nine miles, but at least the carry to our campsite was muddy <\/span><i><span style=\"font-weight: 400;\">and<\/span><\/i><span style=\"font-weight: 400;\"> steep,\u201d I joined in. Our laughter lightened the mood.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The next morning was frosty. Of course. I had to dig past my Hawaiian shirt to find my mittens. Over breakfast, Casey intoned, \u201cWe have to row 34 miles today, but at least all our water froze overnight.\u201d We cracked the layer of ice on our dish buckets with a dead blow hammer, then decided breakfast dishes could wait. The sun was shining and the air was surprisingly calm: we needed to capitalize.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We pushed hard while favorable conditions were present. That didn\u2019t last long, because, remember, the Owyhee isn\u2019t sane. What was sunny blue skies above Montgomery rapid was hail below it.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Mika, whom I had affectionately started referring to as Bad Val, stood up at the oars, pushing wildly. \u201cWe have to row 34 miles on this slow-moving river,\u201d and with a mighty crescendo, she yelled, \u201cbut at least it\u2019s hailing!\u201d\u00a0<\/span><\/p>\n<div id='gallery-3' class='gallery galleryid-37516 gallery-columns-3 gallery-size-thumbnail'><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_2x3_10\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114549\/DTD_Math_JWilhelm_2x3_10-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_2x3_7\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114535\/DTD_Math_JWilhelm_2x3_7-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_2x3_5\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114526\/DTD_Math_JWilhelm_2x3_5-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure>\n\t\t<\/div>\n\n<p><span style=\"font-weight: 400;\">There were a few more snow flurries and some rain, but we kept our spirits up by envisioning the hot springs on the reservoir. And by scheming about how to bum a propane tank from another group. Turns out, we pushed so hard, we pushed past every other group on the water. With 20 miles to make, and over half of them on the lake, we couldn\u2019t afford to wait at Birch Creek to make a trade.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We peeled out of the empty take-out into the already waning current. Mika muttered, \u201cThe propane tank is broken, but at least I get to rig this heavy, awkward, useless motor every day.\u201d<\/span><\/p>\n<p><span style=\"font-weight: 400;\">When we lost the current fully, we strapped our rafts together and party barged. We took turns on the oars, traded DJ duties, told stories and soaked up the suddenly shining sun. We startled a flock of pelicans, who soared away directly overhead. It was a long day of flatwater, and of course, the carry was steep, but at least the hot springs were waiting for our tired muscles. We got camp set up, and Marie peeked her head above the rise.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cWell,\u201d she turned slowly back to us, \u201cWe rowed 13 miles of flatwater into the wind, but at least the hot springs are fully occupied.\u201d<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We laughed. Of course they were.\u00a0<\/span><\/p>\n<div id='gallery-4' class='gallery galleryid-37516 gallery-columns-3 gallery-size-thumbnail'><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_3x2_8\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114438\/DTD_Math_JWilhelm_3x2_8-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_3x2_9\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114443\/DTD_Math_JWilhelm_3x2_9-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_2x3_6\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114530\/DTD_Math_JWilhelm_2x3_6-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/dtd_math_jwilhelm_3x2_7\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114433\/DTD_Math_JWilhelm_3x2_7-100x100.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure>\n\t\t<\/div>\n\n<p><span style=\"font-weight: 400;\">But the thing about the Owyhee, and the wilderness in general, is: anything can happen. And when you have an extra six-pack of Modelos and a bag of Skittles with which to bribe a pair of fishermen leaving the hot springs, truly anything can happen. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">That\u2019s how we found ourselves packed up and river-ready, sitting in a circle around an unlit fire pit, in the pouring rain. The fishermen promised to give us a tow. They said they&#8217;d be back between 10 and 11 am. By 9:50, we had strapped our boats together and built a self-equalizing anchor. We were not making our rescuers wait one single minute. We passed the time spit-balling double negatives from our trip and giggling.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Our rescuers arrived at 10:37 am. They met our shades of neon GORE-TEX\u00ae with jeans and cotton hoodies. They met our self-equalizing anchor with a double overhand knot. And they refused the cash we offered as a thank you. So, we kicked back and relaxed, fully consumed with gratitude and delight.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The Owyhee Canyonlands once again refused to be anything but what they are: stunning and capricious. All we had to do about the latter was double the negatives. It laced each curveball with humor. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">We weren\u2019t bested by the Owyhee this time. Turns out, all we needed was the right math equation.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-37520\" src=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114405\/DTD_Math_JWilhelm_3x2_1-1000x667.jpg\" alt=\"\" width=\"970\" height=\"647\" srcset=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114405\/DTD_Math_JWilhelm_3x2_1-1000x667.jpg 1000w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114405\/DTD_Math_JWilhelm_3x2_1-300x200.jpg 300w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114405\/DTD_Math_JWilhelm_3x2_1-768x512.jpg 768w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114405\/DTD_Math_JWilhelm_3x2_1-1536x1024.jpg 1536w, https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114405\/DTD_Math_JWilhelm_3x2_1.jpg 1800w\" sizes=\"auto, (max-width: 970px) 100vw, 970px\" \/><\/p>\n<p style=\"text-align: center;\">***<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I tried all my tricks. I leaned my ear in close while opening and closing the valve: no sound. I hovered the lighter\u2019s flame near&hellip;<\/p>\n","protected":false},"author":48000,"featured_media":37524,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[336],"tags":[743,38,742,410,316,120],"class_list":["post-37516","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-explore","tag-bad-weather","tag-camping","tag-math-equation","tag-owyhee-river","tag-rafting","tag-women-boaters","post-grid"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Math Equation That Saved Us | Duct Tape Diaries | NRS<\/title>\n<meta name=\"description\" content=\"When things start to go south on Jasmine Wilhelm&#039;s off-season Owyhee trip, her group finds solace in combining negatives to make a positive.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Duct Tape Diaries | The Math Equation That Saved Us\" \/>\n<meta property=\"og:description\" content=\"When things start to go south on Jasmine Wilhelm&#039;s off-season Owyhee trip, her group finds solace in combining negatives to make a positive.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/\" \/>\n<meta property=\"og:site_name\" content=\"Duct Tape Diaries\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/nrsweb\" \/>\n<meta property=\"article:published_time\" content=\"2025-10-14T07:00:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-10-24T17:33:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/10\/24103211\/Owyhee_Math-16x9-1.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1800\" \/>\n\t<meta property=\"og:image:height\" content=\"1013\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Jasmine Wilhelm\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@nrsweb\" \/>\n<meta name=\"twitter:site\" content=\"@nrsweb\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Jasmine Wilhelm\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/\"},\"author\":{\"name\":\"Jasmine Wilhelm\",\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/#\\\/schema\\\/person\\\/5acebaa9c173e9af762aea56401e2292\"},\"headline\":\"The Math Equation That Saved Us\",\"datePublished\":\"2025-10-14T07:00:34+00:00\",\"dateModified\":\"2025-10-24T17:33:41+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/\"},\"wordCount\":1656,\"image\":{\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/d2kl15j267vxtq.cloudfront.net\\\/duct-tape\\\/wp-content\\\/uploads\\\/2025\\\/08\\\/22114424\\\/DTD_Math_JWilhelm_3x2_5.jpg\",\"keywords\":[\"bad weather\",\"camping\",\"math equation\",\"owyhee river\",\"rafting\",\"women boaters\"],\"articleSection\":[\"Explore\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/\",\"url\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/\",\"name\":\"The Math Equation That Saved Us | Duct Tape Diaries | NRS\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/d2kl15j267vxtq.cloudfront.net\\\/duct-tape\\\/wp-content\\\/uploads\\\/2025\\\/08\\\/22114424\\\/DTD_Math_JWilhelm_3x2_5.jpg\",\"datePublished\":\"2025-10-14T07:00:34+00:00\",\"dateModified\":\"2025-10-24T17:33:41+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/#\\\/schema\\\/person\\\/5acebaa9c173e9af762aea56401e2292\"},\"description\":\"When things start to go south on Jasmine Wilhelm's off-season Owyhee trip, her group finds solace in combining negatives to make a positive.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/#primaryimage\",\"url\":\"https:\\\/\\\/d2kl15j267vxtq.cloudfront.net\\\/duct-tape\\\/wp-content\\\/uploads\\\/2025\\\/08\\\/22114424\\\/DTD_Math_JWilhelm_3x2_5.jpg\",\"contentUrl\":\"https:\\\/\\\/d2kl15j267vxtq.cloudfront.net\\\/duct-tape\\\/wp-content\\\/uploads\\\/2025\\\/08\\\/22114424\\\/DTD_Math_JWilhelm_3x2_5.jpg\",\"width\":1800,\"height\":1200},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/2025\\\/10\\\/14\\\/the-math-equation-that-saved-us_2\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"The Math Equation That Saved Us\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/#website\",\"url\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/\",\"name\":\"Duct Tape Diaries\",\"description\":\"Duct Tape Diaries, NRS&#039;s official blog, entertains, educates, inspires and celebrates the paddling lifestyle through compelling storytelling and photography.\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/#\\\/schema\\\/person\\\/5acebaa9c173e9af762aea56401e2292\",\"name\":\"Jasmine Wilhelm\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/99e3319275c5932c3bc5076e0b47a0325f54c8af37418586c834983755966bb5?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/99e3319275c5932c3bc5076e0b47a0325f54c8af37418586c834983755966bb5?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/99e3319275c5932c3bc5076e0b47a0325f54c8af37418586c834983755966bb5?s=96&d=mm&r=g\",\"caption\":\"Jasmine Wilhelm\"},\"description\":\"Jasmine Wilhelm is a freelance writer and river guide. She spends her summers guiding on the Salmon River system, where she learned to boat. In the off-season, you can mostly find her voraciously reading or adventuring on foot.\",\"url\":\"https:\\\/\\\/community.nrs.com\\\/duct-tape\\\/author\\\/jasminewilhelm\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"The Math Equation That Saved Us | Duct Tape Diaries | NRS","description":"When things start to go south on Jasmine Wilhelm's off-season Owyhee trip, her group finds solace in combining negatives to make a positive.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/","og_locale":"en_US","og_type":"article","og_title":"Duct Tape Diaries | The Math Equation That Saved Us","og_description":"When things start to go south on Jasmine Wilhelm's off-season Owyhee trip, her group finds solace in combining negatives to make a positive.","og_url":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/","og_site_name":"Duct Tape Diaries","article_publisher":"https:\/\/www.facebook.com\/nrsweb","article_published_time":"2025-10-14T07:00:34+00:00","article_modified_time":"2025-10-24T17:33:41+00:00","og_image":[{"width":1800,"height":1013,"url":"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/10\/24103211\/Owyhee_Math-16x9-1.jpg","type":"image\/jpeg"}],"author":"Jasmine Wilhelm","twitter_card":"summary_large_image","twitter_creator":"@nrsweb","twitter_site":"@nrsweb","twitter_misc":{"Written by":"Jasmine Wilhelm","Est. reading time":"8 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/#article","isPartOf":{"@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/"},"author":{"name":"Jasmine Wilhelm","@id":"https:\/\/community.nrs.com\/duct-tape\/#\/schema\/person\/5acebaa9c173e9af762aea56401e2292"},"headline":"The Math Equation That Saved Us","datePublished":"2025-10-14T07:00:34+00:00","dateModified":"2025-10-24T17:33:41+00:00","mainEntityOfPage":{"@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/"},"wordCount":1656,"image":{"@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/#primaryimage"},"thumbnailUrl":"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5.jpg","keywords":["bad weather","camping","math equation","owyhee river","rafting","women boaters"],"articleSection":["Explore"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/","url":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/","name":"The Math Equation That Saved Us | Duct Tape Diaries | NRS","isPartOf":{"@id":"https:\/\/community.nrs.com\/duct-tape\/#website"},"primaryImageOfPage":{"@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/#primaryimage"},"image":{"@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/#primaryimage"},"thumbnailUrl":"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5.jpg","datePublished":"2025-10-14T07:00:34+00:00","dateModified":"2025-10-24T17:33:41+00:00","author":{"@id":"https:\/\/community.nrs.com\/duct-tape\/#\/schema\/person\/5acebaa9c173e9af762aea56401e2292"},"description":"When things start to go south on Jasmine Wilhelm's off-season Owyhee trip, her group finds solace in combining negatives to make a positive.","breadcrumb":{"@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/#primaryimage","url":"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5.jpg","contentUrl":"https:\/\/d2kl15j267vxtq.cloudfront.net\/duct-tape\/wp-content\/uploads\/2025\/08\/22114424\/DTD_Math_JWilhelm_3x2_5.jpg","width":1800,"height":1200},{"@type":"BreadcrumbList","@id":"https:\/\/community.nrs.com\/duct-tape\/2025\/10\/14\/the-math-equation-that-saved-us_2\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/community.nrs.com\/duct-tape\/"},{"@type":"ListItem","position":2,"name":"The Math Equation That Saved Us"}]},{"@type":"WebSite","@id":"https:\/\/community.nrs.com\/duct-tape\/#website","url":"https:\/\/community.nrs.com\/duct-tape\/","name":"Duct Tape Diaries","description":"Duct Tape Diaries, NRS&#039;s official blog, entertains, educates, inspires and celebrates the paddling lifestyle through compelling storytelling and photography.","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/community.nrs.com\/duct-tape\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/community.nrs.com\/duct-tape\/#\/schema\/person\/5acebaa9c173e9af762aea56401e2292","name":"Jasmine Wilhelm","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/99e3319275c5932c3bc5076e0b47a0325f54c8af37418586c834983755966bb5?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/99e3319275c5932c3bc5076e0b47a0325f54c8af37418586c834983755966bb5?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/99e3319275c5932c3bc5076e0b47a0325f54c8af37418586c834983755966bb5?s=96&d=mm&r=g","caption":"Jasmine Wilhelm"},"description":"Jasmine Wilhelm is a freelance writer and river guide. She spends her summers guiding on the Salmon River system, where she learned to boat. In the off-season, you can mostly find her voraciously reading or adventuring on foot.","url":"https:\/\/community.nrs.com\/duct-tape\/author\/jasminewilhelm\/"}]}},"_links":{"self":[{"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/posts\/37516","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/users\/48000"}],"replies":[{"embeddable":true,"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/comments?post=37516"}],"version-history":[{"count":15,"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/posts\/37516\/revisions"}],"predecessor-version":[{"id":37555,"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/posts\/37516\/revisions\/37555"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/media\/37524"}],"wp:attachment":[{"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/media?parent=37516"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/categories?post=37516"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/community.nrs.com\/duct-tape\/wp-json\/wp\/v2\/tags?post=37516"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}