{"id":214328,"date":"2025-05-14T06:02:32","date_gmt":"2025-05-14T06:02:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=214328"},"modified":"2025-05-14T06:02:34","modified_gmt":"2025-05-14T06:02:34","slug":"rich-is-driving-from-philadelphia-to-pittsburgh-at-70mph-and-michelle-is-driving-from-pittsburgh-to-philadelphia-at-65mph","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/14\/rich-is-driving-from-philadelphia-to-pittsburgh-at-70mph-and-michelle-is-driving-from-pittsburgh-to-philadelphia-at-65mph\/","title":{"rendered":"Rich is driving from Philadelphia to Pittsburgh at 70mph and Michelle is driving from Pittsburgh to Philadelphia at 65mph"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Rich is driving from Philadelphia to Pittsburgh at 70mph and Michelle is driving from Pittsburgh to Philadelphia at 65mph. If Philadelphia and Pittsburgh are 305 miles apart how long will it take Rich and Michelle to meet?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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 class=\"wp-block-paragraph\">To find out how long it will take Rich and Michelle to meet, we can use the <strong>concept of relative speed<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Given:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Distance between Philadelphia and Pittsburgh = <strong>305 miles<\/strong><\/li>\n\n\n\n<li>Rich\u2019s speed = <strong>70 mph<\/strong><\/li>\n\n\n\n<li>Michelle\u2019s speed = <strong>65 mph<\/strong><\/li>\n\n\n\n<li>They are driving <strong>toward each other<\/strong><\/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>Step 1: Add their speeds (because they are driving toward each other)<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">When two people move toward each other, their <strong>relative speed<\/strong> is the <strong>sum of their individual speeds<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>70\\ \\text{mph (Rich)} + 65\\ \\text{mph (Michelle)} = 135\\ \\text{mph}<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Use the formula for time<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The formula to calculate time is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\text{Time} = \\frac{\\text{Distance}}{\\text{Speed}}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute the known values:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\text{Time} = \\frac{305\\ \\text{miles}}{135\\ \\text{mph}} \\approx 2.26\\ \\text{hours}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Convert <strong>0.26 hours<\/strong> to <strong>minutes<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>0.26 \\times 60 = 15.6 \\text{ minutes} \\approx 16\\ \\text{minutes}<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Answer:<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">They will meet after approximately <strong>2 hours and 16 minutes<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>300-word Explanation:<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This is a classic relative motion problem in which two people are traveling toward one another from different starting points. Rich is driving from Philadelphia at 70 mph, and Michelle is heading from Pittsburgh at 65 mph. The total distance between the two cities is 305 miles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Because they are traveling toward each other, the distance between them decreases at a combined rate \u2014 or relative speed \u2014 which is the sum of their speeds. That means the effective speed at which the gap between them is closing is 70 mph + 65 mph = 135 mph.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find out how long it will take for the two to meet, we divide the total distance (305 miles) by their combined speed (135 mph). This gives us a time of approximately 2.26 hours. Converting the decimal portion (0.26) of the hour into minutes involves multiplying by 60 (since there are 60 minutes in an hour), giving about 15.6 minutes \u2014 which rounds to 16 minutes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, Rich and Michelle will meet approximately 2 hours and 16 minutes after they begin driving toward one another. This type of problem helps reinforce the importance of understanding relative speed and unit conversion in motion scenarios, especially when two objects (or people) are moving simultaneously toward each other. It\u2019s a common application in travel, logistics, and physics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rich is driving from Philadelphia to Pittsburgh at 70mph and Michelle is driving from Pittsburgh to Philadelphia at 65mph. If Philadelphia and Pittsburgh are 305 miles apart how long will it take Rich and Michelle to meet? The Correct Answer And Explanation is: To find out how long it will take Rich and Michelle to [&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-214328","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214328","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=214328"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214328\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}