{"id":227889,"date":"2025-06-06T15:00:54","date_gmt":"2025-06-06T15:00:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227889"},"modified":"2025-06-06T15:00:56","modified_gmt":"2025-06-06T15:00:56","slug":"dave-walked-to-his-friends-house-at-a-rate-of-4-mph-and-returned-biking-at-a-rate-of-10-mph","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/dave-walked-to-his-friends-house-at-a-rate-of-4-mph-and-returned-biking-at-a-rate-of-10-mph\/","title":{"rendered":"Dave walked to his friends house at a rate of 4 mph and returned biking at a rate of 10 mph"},"content":{"rendered":"\n

Dave walked to his friends house at a rate of 4 mph and returned biking at a rate of 10 mph. If it took him 18 minutes longer to walk than bike, what was the total distance of the round trip?<\/p>\n\n\n\n

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

Answer: 12 miles<\/strong><\/p>\n\n\n\n

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

To find the total distance of the round trip, we must determine the distance between Dave\u2019s house and his friend\u2019s house, which we’ll call d<\/strong> miles (one way). Dave walks there at 4 mph<\/strong> and bikes back at 10 mph<\/strong>.<\/p>\n\n\n\n

We know:<\/p>\n\n\n\n

    \n
  • Time = Distance \u00f7 Speed<\/li>\n\n\n\n
  • It took Dave 18 minutes longer<\/strong> to walk than to bike. Since we\u2019re working with speeds in miles per hour, we convert 18 minutes to hours: 18\u00a0minutes=1860=0.3\u00a0hours18\\ \\text{minutes} = \\frac{18}{60} = 0.3\\ \\text{hours}18\u00a0minutes=6018\u200b=0.3\u00a0hours<\/li>\n<\/ul>\n\n\n\n

    Let\u2019s write the expressions for time:<\/p>\n\n\n\n

      \n
    • Time to walk<\/strong> to his friend\u2019s house: d4\\frac{d}{4}4d\u200b<\/li>\n\n\n\n
    • Time to bike<\/strong> back: d10\\frac{d}{10}10d\u200b<\/li>\n<\/ul>\n\n\n\n

      According to the problem:d4=d10+0.3\\frac{d}{4} = \\frac{d}{10} + 0.34d\u200b=10d\u200b+0.3<\/p>\n\n\n\n

      Now, solve this equation:<\/p>\n\n\n\n

        \n
      1. Subtract d10\\frac{d}{10}10d\u200b from both sides: d4\u2212d10=0.3\\frac{d}{4} – \\frac{d}{10} = 0.34d\u200b\u221210d\u200b=0.3<\/li>\n\n\n\n
      2. Find a common denominator: 5d\u22122d20=0.3\u21d23d20=0.3\\frac{5d – 2d}{20} = 0.3 \\Rightarrow \\frac{3d}{20} = 0.3205d\u22122d\u200b=0.3\u21d2203d\u200b=0.3<\/li>\n\n\n\n
      3. Multiply both sides by 20: 3d=63d = 63d=6<\/li>\n\n\n\n
      4. Divide by 3: d=2d = 2d=2<\/li>\n<\/ol>\n\n\n\n

        So, the one-way distance is 2 miles<\/strong>. The total round-trip distance is:2 miles (walked)+2 miles (biked)=4 miles2 \\text{ miles (walked)} + 2 \\text{ miles (biked)} = 4\\ \\text{miles}2 miles (walked)+2 miles (biked)=4 miles<\/p>\n\n\n\n

        Wait! Let\u2019s double-check:<\/p>\n\n\n\n

        The correct interpretation<\/strong> should be:<\/p>\n\n\n\n

          \n
        • ddd is the one-way<\/strong> distance.<\/li>\n\n\n\n
        • So, total round trip<\/strong> distance is 2d=42d = 42d=4 miles.<\/li>\n<\/ul>\n\n\n\n

          Oops\u2014there\u2019s a mistake here. Let’s rework it:<\/p>\n\n\n\n

          Back to:d4=d10+0.3\u21d23d20=0.3\u21d23d=6\u21d2d=2\\frac{d}{4} = \\frac{d}{10} + 0.3 \\Rightarrow \\frac{3d}{20} = 0.3 \\Rightarrow 3d = 6 \\Rightarrow d = 24d\u200b=10d\u200b+0.3\u21d2203d\u200b=0.3\u21d23d=6\u21d2d=2<\/p>\n\n\n\n

          Yes\u2014one way is 2 miles<\/strong>, round trip is 4 miles<\/strong>, not 12 miles<\/strong>.<\/p>\n\n\n\n

          \ud83d\udd01 Corrected Final Answer: 4 miles<\/strong>.<\/p>\n\n\n\n

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

          Dave walked to his friends house at a rate of 4 mph and returned biking at a rate of 10 mph. If it took him 18 minutes longer to walk than bike, what was the total distance of the round trip? The Correct Answer and Explanation is: Answer: 12 miles Explanation To find the total […]<\/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-227889","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227889","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=227889"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227889\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227889"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227889"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227889"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}