{"id":230636,"date":"2025-06-09T18:53:14","date_gmt":"2025-06-09T18:53:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230636"},"modified":"2025-06-09T18:53:16","modified_gmt":"2025-06-09T18:53:16","slug":"one-hour-after-a-hiker-left-a-camp-a-cyclist-set-out-to-catch-up-2","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-2\/","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<\/p>\n\n\n\n

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

Correct Answer:<\/strong><\/h3>\n\n\n\n

The cyclist will catch up with the hiker in 0.5 hours<\/strong> (or 30 minutes<\/strong>) after starting.<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

To solve this problem, we need to understand how the relative motion between the hiker and the cyclist works.<\/p>\n\n\n\n

Let\u2019s break it down step by step.<\/p>\n\n\n\n

\n\n\n\n

Step 1: Define Speeds<\/strong><\/h4>\n\n\n\n
    \n
  • The hiker\u2019s speed = 3 miles per hour (mph)<\/li>\n\n\n\n
  • The cyclist\u2019s speed = 6 mph faster than the hiker = 3 + 6 = 9 mph<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Step 2: Understand the Head Start<\/strong><\/h4>\n\n\n\n

    Since the hiker left one hour earlier<\/strong>, we need to calculate how far the hiker has traveled before the cyclist starts.<\/p>\n\n\n\n

      \n
    • Distance hiker travels in 1 hour = speed \u00d7 time = 3 mph \u00d7 1 hour = 3 miles<\/strong><\/li>\n<\/ul>\n\n\n\n

      So, when the cyclist starts, the hiker is already 3 miles ahead<\/strong>.<\/p>\n\n\n\n

      \n\n\n\n

      Step 3: Set Up a Catch-Up Equation<\/strong><\/h4>\n\n\n\n

      Now we want to find how much time it will take the cyclist to catch up<\/strong> with the hiker after starting.<\/p>\n\n\n\n

      Let ttt be the time in hours<\/strong> the cyclist travels before catching up.<\/p>\n\n\n\n

      In that time:<\/p>\n\n\n\n

        \n
      • The cyclist will travel: 9t9t9t miles<\/li>\n\n\n\n
      • The hiker, continuing at 3 mph, will travel: 3t3t3t miles<\/li>\n<\/ul>\n\n\n\n

        Since the hiker already had a 3-mile head start, the cyclist\u2019s distance must be equal to the hiker\u2019s total distance:Cyclist\u2019s distance=Hiker\u2019s head start+Hiker\u2019s additional distance\\text{Cyclist’s distance} = \\text{Hiker’s head start} + \\text{Hiker’s additional distance}Cyclist\u2019s distance=Hiker\u2019s head start+Hiker\u2019s additional distance9t=3+3t9t = 3 + 3t9t=3+3t<\/p>\n\n\n\n

        \n\n\n\n

        Step 4: Solve the Equation<\/strong><\/h4>\n\n\n\n

        9t=3+3t9t\u22123t=36t=3t=36=0.5 hours9t = 3 + 3t \\\\ 9t – 3t = 3 \\\\ 6t = 3 \\\\ t = \\frac{3}{6} = 0.5 \\text{ hours}9t=3+3t9t\u22123t=36t=3t=63\u200b=0.5 hours<\/p>\n\n\n\n

        \n\n\n\n

        Final Answer<\/strong><\/h4>\n\n\n\n

        It will take the cyclist 0.5 hours<\/strong>, or 30 minutes<\/strong>, to catch up with the hiker after starting<\/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 The Correct Answer and Explanation is: Correct Answer: The cyclist […]<\/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-230636","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230636","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=230636"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230636\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230636"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230636"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}