{"id":22300,"date":"2025-06-16T16:01:37","date_gmt":"2025-06-16T16:01:37","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=22300"},"modified":"2025-06-16T16:01:40","modified_gmt":"2025-06-16T16:01:40","slug":"a-gardener-can-care-for-the-greens-property-in-5-hours","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-gardener-can-care-for-the-greens-property-in-5-hours\/","title":{"rendered":"A gardener can care for the Green&#8217;s property in 5 hours"},"content":{"rendered":"\n<p>A gardener can care for the Green&#8217;s property in 5 hours. If his helper assists him, they can complete the job in 4 hours. How long will it take the helper to do the job?<\/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<p><strong>Correct Answer: 20 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\"><strong>Step-by-step Explanation:<\/strong><\/h3>\n\n\n\n<p>This is a classic <strong>work problem<\/strong> where we calculate how long each person takes to do a job alone or together. Let&#8217;s define the variables and solve:<\/p>\n\n\n\n<p>Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The gardener alone takes <strong>5 hours<\/strong>, so his <strong>work rate<\/strong> is 15\u00a0of\u00a0the\u00a0job\u00a0per\u00a0hour\\frac{1}{5} \\text{ of the job per hour}<\/li>\n\n\n\n<li>The helper&#8217;s time to complete the job alone is <strong>unknown<\/strong>, so let it be <strong>xx<\/strong> hours. Then the helper\u2019s work rate is 1x\u00a0of\u00a0the\u00a0job\u00a0per\u00a0hour\\frac{1}{x} \\text{ of the job per hour}<\/li>\n<\/ul>\n\n\n\n<p>When they work <strong>together<\/strong>, they can finish the job in <strong>4 hours<\/strong>, meaning their <strong>combined rate<\/strong> is 14&nbsp;of&nbsp;the&nbsp;job&nbsp;per&nbsp;hour\\frac{1}{4} \\text{ of the job per hour}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Set up the equation:<\/strong><\/h3>\n\n\n\n<p>Gardener\u2019s&nbsp;rate+Helper\u2019s&nbsp;rate=Combined&nbsp;rate\\text{Gardener&#8217;s rate} + \\text{Helper&#8217;s rate} = \\text{Combined rate} 15+1x=14\\frac{1}{5} + \\frac{1}{x} = \\frac{1}{4}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Solve for xx:<\/strong><\/h3>\n\n\n\n<p>Subtract 15\\frac{1}{5} from both sides: 1x=14\u221215\\frac{1}{x} = \\frac{1}{4} &#8211; \\frac{1}{5}<\/p>\n\n\n\n<p>Find a common denominator: 1x=5\u2212420=120\\frac{1}{x} = \\frac{5 &#8211; 4}{20} = \\frac{1}{20}<\/p>\n\n\n\n<p>So, x=20x = 20<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Answer:<\/strong><\/h3>\n\n\n\n<p>It will take the <strong>helper 20 hours<\/strong> to complete the job alone.<\/p>\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>This problem illustrates the <strong>inverse relationship<\/strong> between time and work rate. The faster someone works (less time needed), the higher their rate. When two people work together, their combined rate is the sum of their individual rates. By turning time into rate and solving algebraically, we can determine how long each person would need if working alone.<\/p>\n\n\n\n<p>This type of problem is commonly seen in time-and-work scenarios, useful in real-life planning of jobs, especially when dealing with teams.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A gardener can care for the Green&#8217;s property in 5 hours. If his helper assists him, they can complete the job in 4 hours. How long will it take the helper to do the job? The correct answer and explanation is: Correct Answer: 20 hours Step-by-step Explanation: This is a classic work problem where we [&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-22300","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22300","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=22300"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22300\/revisions"}],"predecessor-version":[{"id":22301,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22300\/revisions\/22301"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=22300"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=22300"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=22300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}