{"id":6862,"date":"2014-04-01T17:20:50","date_gmt":"2014-04-01T17:20:50","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6862"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-review-of-work-problems","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/04\/01\/math-review-of-work-problems\/","title":{"rendered":"Math Review of Work Problems"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Work problems are types of problems that deal with people or machines that work at different rates of speed.\u00a0 Many of them use a formula that is similar to motion problems. \u00a0The formula w=rt is used relating the rate of work, time, and the work done.\u00a0 Solving story problems involving work combines the steps of reading the story problem, extracting essential data, organizing data into an equation, and solving the equation.<\/p>\n

Reading the Story Problem<\/strong><\/p>\n

Story problems ask questions involving days, hours, or minutes of work.\u00a0 The problem may have people working together or apart to complete a job, as well as the length of time it takes them.\u00a0 Some problems may have machines or objects that work at different rates to complete the same job.\u00a0 For example, suppose that a smaller pipe A can empty a pool in 5 hours.\u00a0 A larger pipe B can empty the pool in 3 hours.\u00a0 How long will it take both pipes together to empty the pool?<\/p>\n

Extracting Essential Data<\/strong><\/p>\n

The solution to this problem is to write an equation that expresses the time it takes both the smaller pipe and the larger pipe to complete the job of emptying the pool.\u00a0 In this example, after 1 hour, Pipe A will empty 1\/5 of the pool, and Pipe B will empty 1\/3 of the pool.\u00a0 In other words, after 1 hour both pipes will empty 1\/3 + 1\/5 of the pool, or 5\/15 + 3\/15 or 8\/15 of the pool.<\/p>\n

Organizing Data into an Equation<\/strong><\/p>\n

Let t equal the amount of time it takes to empty the pool.\u00a0 It will take Pipe A t\/5 to empty the pool and Pipe B t\/3 to empty the pool. It will therefore take both pipes together t\/3 +t\/5 =1 to empty the pool.\u00a0 Since both fractions must have a common denominator, 5t\/15 + 3t\/15 = 1 or 8t\/15 = 1, or 8t = 15.<\/p>\n

Solving the Equation<\/strong><\/p>\n

If 8t =15, then it will take t = 15\/8 hours to empty the pool using both pipes, or 1.875 hours to empty the pool.\u00a0 That is about 1 hour and 52 \u00bd minutes, because .875 of 60 minutes is 52 \u00bd minutes.<\/p>\n

Interested in algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in New Castle, DE: visit Tutoring in New Castle, CO<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview: Work problems are types of problems that deal with people or machines that work at different rates of speed.\u00a0 Many of them use a formula that is similar to motion problems. \u00a0The formula w=rt is used relating the rate of work, time, and the work done.\u00a0 Solving story problems involving work combines the steps […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2649,2652,2651],"class_list":["post-6862","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-story-problems","tag-wrt","tag-work-problems"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6862","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6862"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6862\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}