{"id":230632,"date":"2025-06-09T18:49:00","date_gmt":"2025-06-09T18:49:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230632"},"modified":"2025-06-09T18:49:03","modified_gmt":"2025-06-09T18:49:03","slug":"one-hour-after-a-hiker-left-a-camp-a-cyclist-set-out-to-catch-up","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/one-hour-after-a-hiker-left-a-camp-a-cyclist-set-out-to-catch-up\/","title":{"rendered":"One hour after a hiker left a camp, a cyclist set out to catch up."},"content":{"rendered":"\n

One hour after a hiker left a camp, a cyclist set out to catch up. If the hiker traveled 3 miles per hour and the cyclist traveled 6 miles per hour faster, how long will it take the cyclist to catch up with the hiker? PLEASE HELP!!!!<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

ChatGPT said:<\/h6>\n\n\n\n

\u2705 Correct Answer: 0.5 hours (or 30 minutes)<\/strong><\/h3>\n\n\n\n
\n\n\n\n

\ud83d\udd0d Step-by-Step Explanation:<\/strong><\/h3>\n\n\n\n

We\u2019re given:<\/p>\n\n\n\n

    \n
  • The hiker<\/strong> walks at 3 miles per hour<\/strong>.<\/li>\n\n\n\n
  • The cyclist<\/strong> sets off 1 hour later<\/strong> but travels 6 mph faster<\/strong>, so:\n
      \n
    • Cyclist\u2019s speed = 3 + 6 = 9 miles per hour<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

      We need to find how long it takes the cyclist to catch up with the hiker after the cyclist starts<\/strong>.<\/p>\n\n\n\n

      \n\n\n\n

      \ud83e\udde0 Let\u2019s Define a Variable:<\/h3>\n\n\n\n

      Let t<\/strong> = the number of hours the cyclist<\/strong> travels before catching up.<\/p>\n\n\n\n

      Then during that same time:<\/p>\n\n\n\n

        \n
      • The cyclist<\/strong> travels a distance of:
        distance = speed \u00d7 time = 9 \u00d7 t = 9t<\/code> miles<\/li>\n\n\n\n
      • The hiker<\/strong>, however, has already walked for 1 hour more<\/strong>, so the hiker has been walking for t + 1<\/strong> hours.
        Hiker\u2019s distance: distance = 3 \u00d7 (t + 1) = 3(t + 1)<\/code> miles<\/li>\n<\/ul>\n\n\n\n

        Since they meet when the distances are the same:Cyclist\u2019s distance=Hiker\u2019s distance\\text{Cyclist\u2019s distance} = \\text{Hiker\u2019s distance}Cyclist\u2019s distance=Hiker\u2019s distance9t=3(t+1)9t = 3(t + 1)9t=3(t+1)<\/p>\n\n\n\n

        \n\n\n\n

        \ud83e\uddee Solve the Equation:<\/h3>\n\n\n\n

        Distribute on the right side:9t=3t+39t = 3t + 39t=3t+3<\/p>\n\n\n\n

        Subtract 3t from both sides:6t=36t = 36t=3<\/p>\n\n\n\n

        Divide both sides by 6:t=36=0.5t = \\frac{3}{6} = 0.5t=63\u200b=0.5<\/p>\n\n\n\n

        \n\n\n\n

        \ud83d\udccf Final Answer:<\/h3>\n\n\n\n

        It takes the cyclist 0.5 hours<\/strong>, or 30 minutes<\/strong>, to catch up.<\/p>\n\n\n\n

        \n\n\n\n

        \ud83d\udcd8 Conceptual Explanation (Why This Works):<\/h3>\n\n\n\n

        This problem is about relative speed<\/strong> and distance = rate \u00d7 time<\/strong>. The hiker starts first, so when the cyclist begins, the hiker already has a head start<\/strong>. Since the cyclist is faster, he starts closing the gap at the difference in their speeds<\/strong>, which is 6 mph<\/strong>.<\/p>\n\n\n\n

        In one hour, the hiker walks 3 miles<\/strong>. Since the cyclist closes the gap at 6 miles per hour<\/strong>, it will take:Head startRelative speed=36=0.5 hours\\frac{\\text{Head start}}{\\text{Relative speed}} = \\frac{3}{6} = 0.5 \\text{ hours}Relative speedHead start\u200b=63\u200b=0.5 hours<\/p>\n\n\n\n

        This checks out perfectly!<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        One hour after a hiker left a camp, a cyclist set out to catch up. If the hiker traveled 3 miles per hour and the cyclist traveled 6 miles per hour faster, how long will it take the cyclist to catch up with the hiker? PLEASE HELP!!!! The Correct Answer and Explanation is: ChatGPT said: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-230632","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230632","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=230632"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230632\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230632"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}