{"id":39120,"date":"2025-06-27T02:20:04","date_gmt":"2025-06-27T02:20:04","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39120"},"modified":"2025-06-27T02:20:06","modified_gmt":"2025-06-27T02:20:06","slug":"a-long-distance-runner-started-on-a-course-at-an-average-speed-of-7-mph","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-long-distance-runner-started-on-a-course-at-an-average-speed-of-7-mph\/","title":{"rendered":"A long-distance runner started on a course at an average speed of 7 mph."},"content":{"rendered":"\n
A long-distance runner started on a course at an average speed of 7 mph. Half an hour later, a second runner began the same course at an average speed of 9 mph. How long after the second runner starts will the second runner overtake the first runner<\/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
1.75 hours<\/strong> (or 1 hour and 45 minutes<\/strong>) after the second runner starts.<\/p>\n\n\n\n\n\n\n\n
Explanation<\/strong><\/h3>\n\n\n\n
To solve this problem, we need to determine how long it will take the second runner to catch up with the first runner. Since both are running the same course, we can use the concept of relative speed and distance.<\/p>\n\n\n\n
Let\u2019s break it down step by step.<\/p>\n\n\n\n
Step 1: Find the Head Start<\/strong><\/p>\n\n\n\n
The first runner starts half an hour before the second runner and runs at 7 miles per hour. In half an hour, the first runner covers: Distance=Speed\u00d7Time=7\u2009mph\u00d70.5\u2009hours=3.5\u2009miles\\text{Distance} = \\text{Speed} \\times \\text{Time} = 7 \\, \\text{mph} \\times 0.5 \\, \\text{hours} = 3.5 \\, \\text{miles}Distance=Speed\u00d7Time=7mph\u00d70.5hours=3.5miles<\/p>\n\n\n\n
So, the first runner has a 3.5-mile head start when the second runner begins.<\/p>\n\n\n\n
The second runner is faster and runs at 9 miles per hour. The first runner runs at 7 miles per hour. The relative speed of the second runner compared to the first is: 9\u2009mph\u22127\u2009mph=2\u2009mph9 \\, \\text{mph} – 7 \\, \\text{mph} = 2 \\, \\text{mph}9mph\u22127mph=2mph<\/p>\n\n\n\n
This means the second runner reduces the gap by 2 miles every hour.<\/p>\n\n\n\n
Step 3: Calculate Time to Close the Gap<\/strong><\/p>\n\n\n\n
To find out how long it takes the second runner to cover the 3.5-mile head start with a relative speed of 2 mph, we use: Time=DistanceSpeed=3.5\u2009miles2\u2009mph=1.75\u2009hours\\text{Time} = \\frac{\\text{Distance}}{\\text{Speed}} = \\frac{3.5 \\, \\text{miles}}{2 \\, \\text{mph}} = 1.75 \\, \\text{hours}Time=SpeedDistance\u200b=2mph3.5miles\u200b=1.75hours<\/p>\n\n\n\n
Final Answer<\/strong><\/p>\n\n\n\n
The second runner will overtake the first runner 1.75 hours<\/strong> after starting. Converting 0.75 hours into minutes (0.75 \u00d7 60), we get 45 minutes<\/strong>, so the second runner overtakes the first 1 hour and 45 minutes<\/strong> after starting.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
A long-distance runner started on a course at an average speed of 7 mph. Half an hour later, a second runner began the same course at an average speed of 9 mph. How long after the second runner starts will the second runner overtake the first runner The Correct Answer and Explanation is: Correct Answer: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-39120","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39120","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=39120"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39120\/revisions"}],"predecessor-version":[{"id":39122,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39120\/revisions\/39122"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39120"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39120"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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