{"id":230098,"date":"2025-06-08T19:43:59","date_gmt":"2025-06-08T19:43:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230098"},"modified":"2025-06-08T19:44:01","modified_gmt":"2025-06-08T19:44:01","slug":"aliza-needs-to-run-at-a-rate-faster-than-8-8-feet-per-second-in-order-to-exceed-her-fastest-time-in-a-race","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/aliza-needs-to-run-at-a-rate-faster-than-8-8-feet-per-second-in-order-to-exceed-her-fastest-time-in-a-race\/","title":{"rendered":"Aliza needs to run at a rate faster than 8.8 feet per second in order to exceed her fastest time in a race"},"content":{"rendered":"\n<p>Aliza needs to run at a rate faster than 8.8 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:<\/p>\n\n\n\n<p>He concludes that she is not running fast enough to exceed her fastest time. What errors did the coach make? Check all that apply. He used an incorrect time ratio converting hours to minutes. His units do not cancel. He used an incorrect distance ratio converting miles to feet. He incorrectly concluded that she is not running fast enough. He cannot determine her average rate in miles per hour after only 15 minutes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-307.png\" alt=\"\" class=\"wp-image-230100\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2705 He used an incorrect time ratio converting hours to minutes.<\/li>\n\n\n\n<li>\u2705 His units do not cancel.<\/li>\n\n\n\n<li>\u2705 He incorrectly concluded that she is not running fast enough.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>In this problem, Aliza\u2019s coach attempts to determine whether she is running faster than 8.8 feet per second (ft\/s) by converting her average speed of <strong>5.8 miles per hour (mph)<\/strong> into ft\/s. However, his unit conversion contains a <strong>critical time conversion error<\/strong>, which leads to a faulty conclusion.<\/p>\n\n\n\n<p>Let\u2019s examine the coach\u2019s setup:5.8&nbsp;mi\/h\u00d7(1&nbsp;h15&nbsp;min)\u00d7(5280&nbsp;ft1&nbsp;mi)\u00d7(1&nbsp;min60&nbsp;s)5.8 \\text{ mi\/h} \\times \\left(\\frac{1 \\text{ h}}{15 \\text{ min}}\\right) \\times \\left(\\frac{5280 \\text{ ft}}{1 \\text{ mi}}\\right) \\times \\left(\\frac{1 \\text{ min}}{60 \\text{ s}}\\right)5.8&nbsp;mi\/h\u00d7(15&nbsp;min1&nbsp;h\u200b)\u00d7(1&nbsp;mi5280&nbsp;ft\u200b)\u00d7(60&nbsp;s1&nbsp;min\u200b)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Error 1: Incorrect Time Conversion<\/strong><\/h3>\n\n\n\n<p>The term 1&nbsp;h15&nbsp;min\\frac{1 \\text{ h}}{15 \\text{ min}}15&nbsp;min1&nbsp;h\u200b is incorrect. Since 1 hour = 60 minutes, this should be reversed. If converting miles per hour to feet per second, the time conversions should use the correct unit ratios:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\u00a0hour=60\u00a0minutes=3600\u00a0seconds1 \\text{ hour} = 60 \\text{ minutes} = 3600 \\text{ seconds}1\u00a0hour=60\u00a0minutes=3600\u00a0seconds<br>Thus, <strong>the correct conversion<\/strong> would be:<\/li>\n<\/ul>\n\n\n\n<p>5.8&nbsp;mi\/h\u00d7(5280&nbsp;ft1&nbsp;mi)\u00d7(1&nbsp;h3600&nbsp;s)5.8 \\text{ mi\/h} \\times \\left(\\frac{5280 \\text{ ft}}{1 \\text{ mi}}\\right) \\times \\left(\\frac{1 \\text{ h}}{3600 \\text{ s}}\\right)5.8&nbsp;mi\/h\u00d7(1&nbsp;mi5280&nbsp;ft\u200b)\u00d7(3600&nbsp;s1&nbsp;h\u200b)<\/p>\n\n\n\n<p>This results in:5.8\u00d75280\/3600\u22488.5&nbsp;ft\/s5.8 \\times 5280 \/ 3600 \\approx 8.5 \\text{ ft\/s}5.8\u00d75280\/3600\u22488.5&nbsp;ft\/s<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Error 2: Units Do Not Cancel Correctly<\/strong><\/h3>\n\n\n\n<p>Because the time conversion was incorrect, the units do not cancel properly, resulting in a meaningless unit (not feet per second). This shows a fundamental error in dimensional analysis.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Error 3: Incorrect Conclusion<\/strong><\/h3>\n\n\n\n<p>After correcting the math, we find that Aliza is running at approximately <strong>8.5 ft\/s<\/strong>, which is <strong>very close to<\/strong> the target of <strong>8.8 ft\/s<\/strong>. Given slight variations, this may be <strong>fast enough<\/strong>, and his conclusion is premature.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Note<\/strong><\/h3>\n\n\n\n<p>The coach <strong>can<\/strong> determine her average speed after 15 minutes (since average speed is total distance\/time), so that statement is incorrect.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-724.jpeg\" alt=\"\" class=\"wp-image-230102\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Aliza needs to run at a rate faster than 8.8 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown [&hellip;]<\/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-230098","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230098","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=230098"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230098\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}