{"id":2844,"date":"2022-08-26T07:57:58","date_gmt":"2022-08-26T11:57:58","guid":{"rendered":"https:\/\/josmfs.net\/?p=2844"},"modified":"2024-04-06T12:42:06","modified_gmt":"2024-04-06T16:42:06","slug":"skating-rendezvous-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/08\/26\/skating-rendezvous-problem\/","title":{"rendered":"Skating Rendezvous Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2842\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/08\/Skating-Rendezvous-Fig2.jpg\" alt=\"\" width=\"200\" height=\"212\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/08\/Skating-Rendezvous-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/08\/Skating-Rendezvous-Fig2-284x300.jpg 284w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is a fun problem from the 1989 American Invitational Mathematics Exam (AIME).<\/p>\n<p>\u201cTwo skaters, Allie and Billie, are at points <em>A<\/em> and <em>B<\/em>, respectively, on a flat, frozen lake. The distance between <em>A<\/em> and <em>B<\/em> is 100 meters. Allie leaves <em>A<\/em> and skates at a speed of 8 meters per second on a straight line that makes a 60\u00b0 angle with <em>AB<\/em>. At the same time Allie leaves <em>A<\/em>, Billie leaves <em>B<\/em> at a speed of 7 meters per second and follows the straight path that produces the earliest possible meeting of the two skaters, given their speeds. How many meters does Allie skate before meeting Billie?\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Skating-Rendezvous-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/08\/Skating-Rendezvous-Problem-220314.pdf\">Skating Rendezvous Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a fun problem from the 1989 American Invitational Mathematics Exam (AIME). \u201cTwo skaters, Allie and Billie, are at points A and B, respectively, on a flat, frozen lake. The distance between A and B is 100 meters. Allie leaves A and skates at a speed of 8 meters per second on a straight [&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":[238,81],"class_list":["post-2844","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-aime","tag-travel-puzzles"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2844","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=2844"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2844\/revisions"}],"predecessor-version":[{"id":3601,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2844\/revisions\/3601"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}