{"id":276099,"date":"2025-07-30T16:00:52","date_gmt":"2025-07-30T16:00:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=276099"},"modified":"2025-07-30T16:00:55","modified_gmt":"2025-07-30T16:00:55","slug":"a-cyclist-traveled-70-km-moving-at-a-constant-speed","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/30\/a-cyclist-traveled-70-km-moving-at-a-constant-speed\/","title":{"rendered":"A cyclist traveled 70 km moving at a constant speed"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Here are the correct answers for the problem:<\/p>\n\n\n\n

v(t) = 70\/t
v(5) = 14
v(7) = 10
v(3.5) = 20<\/p>\n\n\n\n

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

This problem requires understanding the fundamental relationship between distance, speed, and time. The formula that connects these three variables is:<\/p>\n\n\n\n

Distance = Speed \u00d7 Time<\/p>\n\n\n\n

In this scenario, we are given:<\/p>\n\n\n\n

    \n
  • Distance (d):<\/strong>\u00a0A constant 70 km.<\/li>\n\n\n\n
  • Speed (v):<\/strong>\u00a0The variable we need to express as a function of time.<\/li>\n\n\n\n
  • Time (t):<\/strong>\u00a0The variable on which the speed depends.<\/li>\n<\/ul>\n\n\n\n

    1. Deriving the Formula for v(t)<\/strong><\/p>\n\n\n\n

    To find the formula that shows the dependence of speed (v) on time (t), we start with the basic equation and substitute the known distance:<\/p>\n\n\n\n

    70 = v \u00d7 t<\/p>\n\n\n\n

    Our goal is to isolate the speed (v) on one side of the equation to define it as a function of time, written as v(t). To do this, we divide both sides of the equation by time (t):<\/p>\n\n\n\n

    v = 70 \/ t<\/p>\n\n\n\n

    Therefore, the formula for the speed as a function of time is:
    v(t) = 70\/t<\/strong><\/p>\n\n\n\n

    This formula shows that speed and time are inversely proportional. To cover a fixed distance, if the travel time increases, the required speed decreases, and if the travel time decreases, the required speed must be higher.<\/p>\n\n\n\n

    2. Calculating the Specific Values<\/strong><\/p>\n\n\n\n

    Now, we use the derived formula v(t) = 70\/t to find the speed for the given time values.<\/p>\n\n\n\n

      \n
    • Find v(5):<\/strong>
      We substitute t = 5 into the formula:
      v(5) = 70 \/ 5 =\u00a014<\/strong>
      This means if the cyclist takes 5 hours, their constant speed must be 14 km\/h.<\/li>\n\n\n\n
    • Find v(7):<\/strong>
      We substitute t = 7 into the formula:
      v(7) = 70 \/ 7 =\u00a010<\/strong>
      If the trip takes 7 hours, the cyclist\u2019s speed must be 10 km\/h.<\/li>\n\n\n\n
    • Find v(3.5):<\/strong>
      We substitute t = 3.5 into the formula:
      v(3.5) = 70 \/ 3.5 =\u00a020<\/strong>
      If the cyclist completes the journey in just 3.5 hours, their speed must be 20 km\/h.<\/li>\n<\/ul>\n\n\n\n
      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      The Correct Answer and Explanation is: Here are the correct answers for the problem: v(t) = 70\/tv(5) = 14v(7) = 10v(3.5) = 20 Explanation: This problem requires understanding the fundamental relationship between distance, speed, and time. The formula that connects these three variables is: Distance = Speed \u00d7 Time In this scenario, we are given: […]<\/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-276099","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/276099","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=276099"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/276099\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=276099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=276099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=276099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}