{"id":168830,"date":"2024-11-18T12:42:14","date_gmt":"2024-11-18T12:42:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168830"},"modified":"2024-11-18T12:42:16","modified_gmt":"2024-11-18T12:42:16","slug":"what-is-the-greatest-amount-of-time-it-takes-the-painters-to-paint-the-room-together","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/18\/what-is-the-greatest-amount-of-time-it-takes-the-painters-to-paint-the-room-together\/","title":{"rendered":"What is the greatest amount of time it takes the painters to paint the room together"},"content":{"rendered":"\n<p>What is the greatest amount of time it takes the painters to paint the room together?<br>The inequality to model this situation is: 1\/3+1\/6 ? 1\/x<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to find the greatest amount of time it takes the painters to paint the room together. The inequality provided is:<\/p>\n\n\n\n<p>[<br>\\frac{1}{3} + \\frac{1}{6} \\leq \\frac{1}{x}<br>]<\/p>\n\n\n\n<p>Here, (\\frac{1}{3}) and (\\frac{1}{6}) represent the rates at which the two painters work individually, and (x) represents the time it would take for them to paint the room together.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Understanding the Rates<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first painter can paint the room in 3 hours, meaning that in 1 hour, they can paint (\\frac{1}{3}) of the room.<\/li>\n\n\n\n<li>The second painter can paint the room in 6 hours, so in 1 hour, they can paint (\\frac{1}{6}) of the room.<\/li>\n<\/ul>\n\n\n\n<p>Together, in 1 hour, they will paint the sum of these fractions:<\/p>\n\n\n\n<p>[<br>\\frac{1}{3} + \\frac{1}{6}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Adding the Fractions<\/h3>\n\n\n\n<p>To add (\\frac{1}{3}) and (\\frac{1}{6}), we need a common denominator. The least common denominator of 3 and 6 is 6. We can rewrite (\\frac{1}{3}) as (\\frac{2}{6}) to have the same denominator:<\/p>\n\n\n\n<p>[<br>\\frac{1}{3} = \\frac{2}{6}<br>]<\/p>\n\n\n\n<p>Now, add the two fractions:<\/p>\n\n\n\n<p>[<br>\\frac{2}{6} + \\frac{1}{6} = \\frac{3}{6} = \\frac{1}{2}<br>]<\/p>\n\n\n\n<p>So, together, the painters can paint (\\frac{1}{2}) of the room in one hour.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solving for (x)<\/h3>\n\n\n\n<p>The equation tells us that the combined rate of the two painters is (\\frac{1}{x}), where (x) is the time it takes for them to paint the entire room together. Since they paint (\\frac{1}{2}) of the room in one hour, we set up the following equation:<\/p>\n\n\n\n<p>[<br>\\frac{1}{x} = \\frac{1}{2}<br>]<\/p>\n\n\n\n<p>To solve for (x), we can take the reciprocal of both sides:<\/p>\n\n\n\n<p>[<br>x = 2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The greatest amount of time it takes the painters to paint the room together is <strong>2 hours<\/strong>. This means that if both painters work together, they can finish painting the room in 2 hours.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the greatest amount of time it takes the painters to paint the room together?The inequality to model this situation is: 1\/3+1\/6 ? 1\/x The Correct Answer and Explanation is: To solve this problem, we need to find the greatest amount of time it takes the painters to paint the room together. The inequality [&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-168830","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168830","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=168830"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168830\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168830"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168830"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}