{"id":2042,"date":"2021-02-27T09:54:22","date_gmt":"2021-02-27T14:54:22","guid":{"rendered":"http:\/\/josmfs.net\/?p=2042"},"modified":"2024-04-08T09:30:20","modified_gmt":"2024-04-08T13:30:20","slug":"three-runners-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/02\/27\/three-runners-puzzle\/","title":{"rendered":"Three Runners Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2040\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/02\/Three-Runners-Puzzle-Fig2.jpg\" alt=\"\" width=\"239\" height=\"108\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/02\/Three-Runners-Puzzle-Fig2.jpg 402w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/02\/Three-Runners-Puzzle-Fig2-300x136.jpg 300w\" sizes=\"auto, (max-width: 239px) 100vw, 239px\" \/>Here is another <a href=\"https:\/\/mindyourdecisions.com\/blog\/2019\/12\/26\/three-runners-puzzle-from-indias-civil-services-exam\">problem<\/a> from Presh Talwalkar which he says is adapted from India\u2019s Civil Services Exam.<\/p>\n<p>\u201cThere are three runners X, Y, and Z. Each runs with a different uniform speed in a 1000 meters race.\u00a0 If X gives Y a start of 50 meters, they will finish the race at the same time.\u00a0 If X gives Z a start of 69 meters, they will finish the race at the same time.\u00a0 Suppose Y and Z are in a [1000 meter] race. How much of a start should Y give to Z so they would finish the race at the same time?\u201d<\/p>\n<p>Even though Talwalkar\u2019s original graphic showed all the runners in a 1000 meter race, it was not immediately clear to me from the wording that the race between Y and Z was also 1000 meters.\u00a0 But that was the case, so I made it explicit.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Three-Runners-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/02\/Three-Runners-Puzzle-191227.pdf\">Three Runners Puzzle<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another problem from Presh Talwalkar which he says is adapted from India\u2019s Civil Services Exam. \u201cThere are three runners X, Y, and Z. Each runs with a different uniform speed in a 1000 meters race.\u00a0 If X gives Y a start of 50 meters, they will finish the race at the same time.\u00a0 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[17,81],"class_list":["post-2042","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-presh-talwalkar","tag-travel-puzzles"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2042","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2042"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2042\/revisions"}],"predecessor-version":[{"id":3699,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2042\/revisions\/3699"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}