{"id":6860,"date":"2014-04-02T16:25:04","date_gmt":"2014-04-02T16:25:04","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6860"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-review-of-motion-problems","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/04\/02\/math-review-of-motion-problems\/","title":{"rendered":"Math Review of Motion Problems"},"content":{"rendered":"

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

Motion problems are special types of rational expressions that are based on the relationship between distance, rate, and time (d=rt).\u00a0 In order to solve them, it is important to read the story problem, recognize the essential information, and organize the facts in an equation.<\/p>\n

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

Story problems usually contain all the information that is necessary, and sometimes additional information that is not needed.\u00a0 If the problem involves the speed of something traveling, people or vehicles either going in opposite directions or overtaking each other, and a rate of speed that may change or differ, it will follow the distance = rate X time pattern.\u00a0 Suppose two drivers start out at the same time travelling in opposite directions.\u00a0 One driver was driving 6 miles slower than the other driver.\u00a0 After 10 hours they were 940 miles apart.\u00a0 Find the speed each driver was driving.<\/p>\n

Recognizing the Essential Information<\/strong><\/p>\n

In the sample story problem, there are several things that are known.\u00a0 First, the total distance, 940 miles, is known.\u00a0 Second, the time for each driver is known (10 hours).\u00a0 If Driver A is going r miles per hour, Driver B is going r-6 miles per hour.\u00a0 We know the rate is miles per hour rather than feet per second or kilometers per hour, because the time traveled is measured in hours and the distance measured is measured in miles.<\/p>\n

Organizing the Data<\/strong><\/p>\n

The data can then be organized in an equation.\u00a0 If d=rt, the value for d, 940 miles, is already known. That is the same value for both Driver A and Driver B.\u00a0 In addition, we also know that the time for both drivers is the same (10 hours).\u00a0 The rate for Driver A is r and the rate for Driver B is r-6.\u00a0 In order to set up the equation so that both Driver A and Driver B are included, the equation would then be 10r (the rate of Driver A) + 10(r-6) (the rate of Driver B) = 940.<\/p>\n

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

The equation, 10r + 10(r-6) = 940, can be expanded to 10r +10r -60 =940.\u00a0 Then like terms can be combined as 20r \u2013 60 = 940.\u00a0 Then 60 can be added to each side so that 20r = 940 + 60 or 20r = 1000.\u00a0 Dividing both sides by 20, r equals 50 and r \u2013 6 = 44.\u00a0 Also, 20(50) – 60 = 940.<\/p>\n

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Overview: Motion problems are special types of rational expressions that are based on the relationship between distance, rate, and time (d=rt).\u00a0 In order to solve them, it is important to read the story problem, recognize the essential information, and organize the facts in an equation. Reading the Story Problem Story problems usually contain all the […]<\/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":[2650,2648,2649],"class_list":["post-6860","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-drt","tag-motion-problems","tag-story-problems"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6860","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=6860"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6860\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6860"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6860"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}