{"id":18471,"date":"2025-06-13T00:17:59","date_gmt":"2025-06-13T00:17:59","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=18471"},"modified":"2025-06-13T00:18:01","modified_gmt":"2025-06-13T00:18:01","slug":"one-car-went-10-miles-farther-when-traveling-at-50-mph-than-a-second-car-that-traveled-2-hours-longer-at-a-speed-of-40-mph","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/one-car-went-10-miles-farther-when-traveling-at-50-mph-than-a-second-car-that-traveled-2-hours-longer-at-a-speed-of-40-mph\/","title":{"rendered":"One car went 10 miles farther when traveling at 50 mph than a second car that traveled 2 hours longer at a speed of 40 mph"},"content":{"rendered":"\n<p>One car went 10 miles farther when traveling at 50 mph than a second car that traveled 2 hours longer at a speed of 40 mph. How long did the first car travel?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Correct Answer: <strong>5 hours<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u270d\ufe0f Explanation:<\/h3>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>First car:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Speed = 50 mph<\/li>\n\n\n\n<li>Distance = 10 miles more than the second car<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Second car:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Speed = 40 mph<\/li>\n\n\n\n<li>Time = 2 hours more than the first car<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Let\u2019s <strong>let the time the first car traveled be<\/strong>:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>x hours<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>Then, the <strong>time the second car traveled<\/strong> is:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>x + 2 hours<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Now, we use the <strong>distance formula<\/strong>: Distance=Speed\u00d7Time\\text{Distance} = \\text{Speed} \\times \\text{Time}<\/p>\n\n\n\n<p>So,<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Distance of <strong>first car<\/strong> = 50x50x<\/li>\n\n\n\n<li>Distance of <strong>second car<\/strong> = 40(x+2)40(x + 2)<\/li>\n<\/ul>\n\n\n\n<p>We are told the first car traveled <strong>10 miles farther<\/strong>: 50x=40(x+2)+1050x = 40(x + 2) + 10<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\uddee Solve the equation:<\/h3>\n\n\n\n<p>Expand the right-hand side: 50x=40x+80+1050x = 40x + 80 + 10 50x=40x+9050x = 40x + 90<\/p>\n\n\n\n<p>Subtract 40x from both sides: 10x=9010x = 90<\/p>\n\n\n\n<p>Divide both sides by 10: x=9x = 9<\/p>\n\n\n\n<p>Wait! That gives us <strong>x = 9<\/strong>, not 5. Let&#8217;s double-check.<\/p>\n\n\n\n<p>Ah! There was a <strong>miscalculation<\/strong>. Let&#8217;s correct it from the equation step.<\/p>\n\n\n\n<p>Actually, the correct equation should be: 50x=40(x+2)+1050x = 40(x + 2) + 10 50x=40x+80+1050x = 40x + 80 + 10 50x=40x+9050x = 40x + 90<\/p>\n\n\n\n<p>Subtract 40x: 10x=90\u21d2x=910x = 90 \\Rightarrow x = 9<\/p>\n\n\n\n<p>\u2705 <strong>Corrected Answer: 9 hours<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer: <strong>9 hours<\/strong><\/h3>\n\n\n\n<p>So, the first car traveled for <strong>9 hours<\/strong>, covering a distance of: 50\u00d79=450&nbsp;miles50 \\times 9 = 450 \\text{ miles}<\/p>\n\n\n\n<p>And the second car traveled for: 9+2=11&nbsp;hours\u21d240\u00d711=440&nbsp;miles9 + 2 = 11 \\text{ hours} \\Rightarrow 40 \\times 11 = 440 \\text{ miles}<\/p>\n\n\n\n<p>This confirms the first car went <strong>10 miles farther<\/strong> than the second.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One car went 10 miles farther when traveling at 50 mph than a second car that traveled 2 hours longer at a speed of 40 mph. How long did the first car travel? The correct answer and explanation is: \u2705 Correct Answer: 5 hours \u270d\ufe0f Explanation: We are given: Let\u2019s let the time the first [&hellip;]<\/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-18471","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18471","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=18471"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18471\/revisions"}],"predecessor-version":[{"id":18472,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18471\/revisions\/18472"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}