{"id":9119,"date":"2017-04-02T00:32:54","date_gmt":"2017-04-02T00:32:54","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=9119"},"modified":"2017-04-02T00:32:54","modified_gmt":"2017-04-02T00:32:54","slug":"math-review-of-uniform-motion-problems","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2017\/04\/02\/math-review-of-uniform-motion-problems\/","title":{"rendered":"Math Review of Uniform Motion Problems"},"content":{"rendered":"

Overview<\/strong><\/h3>\n

Problem-solving strategies can also be used to solve uniform motion problems that use the relationship between distance, rate, and time.\u00a0 Students can first understand the problem, develop and carry out a plan, find the answer, and then check the answer.<\/p>\n

Understand the Problem<\/strong><\/h3>\n

Suppose one car leaves Calgary, Alberta, Canada traveling north at 56 kilometers per hour.\u00a0 Another car leaves Calgary one hour later, on the same road, but is traveling at a speed of 84 kilometers per hour.\u00a0 How far will they be from Calgary when the faster car meets the first?\u00a0 This is a uniform motion problem, using the equation distance (d) = rate (r) x time (t).\u00a0\u00a0 In Canada, the rate of speed is measured by using the metric system, or kilometers per hour.\u00a0 The question is:\u00a0 How far will the cars be from Calgary when they meet?\u00a0 The data; the fast car leaves 1 hour after the slow car; the slow car travels at 56 km\/h; the fast car travels at 84 km\/h.\u00a0 Both cars start at the same place, are traveling the same distance, and going in the same direction, so that information is not relevant to the problem.<\/p>\n

\"Calgary\"<\/a><\/h3>\n

 <\/p>\n

Develop a Plan<\/strong><\/h3>\n

Draw a diagram using the data.\u00a0 The distances for both the fast car and the slow car are the same, so in this case d represents the distance traveled by both cars when they meet.\u00a0 If t is the time for the fast car, then t +1 is the time for the slow car.\u00a0 Therefore, there are two equations, d = 56(t +1) and d = 84t.<\/p>\n

<\/h3>\n

Find the Answer<\/strong><\/h3>\n

Since there are two equivalent equations, the substitution method can be used such that 56t +56 = 84t.\u00a0 Simplifying, 56 = 84t-56t = 28t, 56\/28 = t, t =2, or in about 2 hours.\u00a0 Now that the time is known, the distance in kilometers can be calculated using either equation. Using the second equation for the faster car, the distance is 84(2) = 168 km, another 30 km or so past Red Deer.<\/p>\n

<\/h3>\n

Check the Answer<\/strong><\/h3>\n

In order to check the answer, check to see if the equations make sense. 168 is equal to 56(3), or in other words, 168=56(1 +2), and 84 (2) = 168.\u00a0 Incidentally, 56 km\/h is almost 35 miles an hour and 84 km\/h is about 52 miles an hour.<\/p>\n

<\/h1>\n

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SchoolTutoring Academy<\/a>\u00a0<\/span><\/strong>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 Red Deer, AB, Canada: visit:\u00a0 Tutoring in Red Deer, AB<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Problem-solving strategies can also be used to solve uniform motion problems that use the relationship between distance, rate, and time.\u00a0 Students can first understand the problem, develop and carry out a plan, find the answer, and then check the answer. Understand the Problem Suppose one car leaves Calgary, Alberta, Canada traveling north at 56 […]<\/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":[515,1391,4022,4023,4024],"class_list":["post-9119","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-distance","tag-problem-solving","tag-rate","tag-time","tag-uniform-motion"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/9119","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=9119"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/9119\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=9119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=9119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=9119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}