{"id":5456,"date":"2015-01-15T09:00:23","date_gmt":"2015-01-15T17:00:23","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=5456"},"modified":"2020-01-15T10:48:20","modified_gmt":"2020-01-15T18:48:20","slug":"one-more-rtd-table-problem-average-rates-part-2","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/one-more-rtd-table-problem-average-rates-part-2\/","title":{"rendered":"One More RTD Table Problem: Average Rates Part 2"},"content":{"rendered":"<p>If you haven&#8217;t been following our series on RTD tables, take a few minutes to catch up:<\/p>\n<ul>\n<li><a href=\"https:\/\/magoosh.com\/gmat\/using-diagrams-to-solve-gmat-rate-problems-part-1\/\">Using Diagrams to Solve Rate Problems: Part 1<\/a><\/li>\n<li><a href=\"https:\/\/magoosh.com\/gmat\/using-diagrams-to-solve-gmat-rate-problems-part-2\/\">Using Diagrams to Solve Rate Problems: Part 2<\/a><\/li>\n<li><a href=\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-1\/\">A Different Use of the RTD Table: Part 1<\/a><\/li>\n<li><a href=\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/\">A Different Use of the RTD Table: Part 2<\/a><\/li>\n<li><a href=\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/\">Using the RTD Table for a Complicated Problem<\/a><\/li>\n<li><a href=\"https:\/\/magoosh.com\/gmat\/one-more-rtd-table-problem-average-rates-part-1\/\">One More RTD Table Problem: Average Rates Part 1<\/a><\/li>\n<\/ul>\n<p>Yesterday we solved <a href=\"https:\/\/magoosh.com\/gmat\/one-more-rtd-table-problem-average-rates-part-1\/\">this problem<\/a>:<\/p>\n<p><em>Div\u2019s bicycle tour consists of three legs of equal length.\u00a0 For the first leg Div averaged 16 kilometers per hour. For the second leg he averaged 24 kilometers per hour. What speed must Div average for the final leg in order to average 24 kilometers per hour for the entire tour? <\/em><\/p>\n<p><em>A) 20 kilometers per hour<\/em><br \/>\n<em>B) 28 kilometers per hour<\/em><br \/>\n<em>C) 32 kilometers per hour<\/em><br \/>\n<em>D) 40 kilometers per hour<\/em><br \/>\n<em>E) 48 kilometers per hour<\/em><\/p>\n<p>We made a pretty good use of the RTD table, but we still took quite a while to arrive at our answer, and we did a lot of computation and algebra, every step inviting some sort of error.<\/p>\n<p>There are two shortcuts that could save us some time and energy while reducing opportunities for computational error.<\/p>\n<p>&nbsp;<\/p>\n<h2>The big shortcut.<\/h2>\n<p>Notice that this problem doesn\u2019t specify the lengths of the legs, but that every answer is a constant. That implies that <em>so long as the legs are all of the same length<\/em> as required by the problem, <em>any leg length will yield the same answer.<\/em><\/p>\n<p>Let\u2019s take advantage of that fact to avoid some unnecessary algebra. Let\u2019s stipulate an easy leg length.\u00a0 What leg length would be easiest to work with? 48 kilometers, since 48 is the least common multiple of 16 and 24.<\/p>\n<p>&nbsp;<\/p>\n<h2>Filling in the table.<\/h2>\n<p>Now we can put constants in the cells for leg lengths as well as in some of the cells for rates.<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-7344 size-medium\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-1-300x153.png\" alt=\"table-1\" width=\"300\" height=\"153\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-1-300x153.png 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-1-600x306.png 600w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-1.png 756w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>We can also determine a time for the bottom row\u2014a combined time for all three legs\u2014by dividing the combined distance by the average rate.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-7346\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-2-300x157.png\" alt=\"table-2\" width=\"300\" height=\"157\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-2-300x157.png 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-2-600x315.png 600w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-2.png 740w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>That allows us to determine the time for the third leg, since the sum of the times for the three legs is the combined time for the tour.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-7347\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-3-300x153.png\" alt=\"table-3\" width=\"300\" height=\"153\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-3-300x153.png 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-3-600x306.png 600w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-3.png 746w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Finally, we can determine the rate for the third leg by dividing the distance by the time.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-7348\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-4-300x149.png\" alt=\"table-4\" width=\"300\" height=\"149\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-4-300x149.png 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-4-600x298.png 600w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/table-4.png 750w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2>The little shortcut.<\/h2>\n<p>The little shortcut isn\u2019t as powerful as the big one, and it\u2019s peculiar to average problems, so you won\u2019t get much use out of it, but here it is.<\/p>\n<p>Since the rate for the second leg is equal to the average rate, we can ignore that leg. Because Div averages 24 kph for the entire tour and 24 kph for the second leg, he must also average 24 kph for the balance of the tour. So we could leave the second leg out altogether.<\/p>\n<p>What would the RTD table for that amended problem look like? Well, if we use the big shortcut, we\u2019ll still probably make each leg 48 kilometers, since 48 is the least common denominator of the rate in kph of the first leg and the rate in kph of the entire tour.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-7349\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-1-300x124.png\" alt=\"short-table-1\" width=\"300\" height=\"124\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-1-300x124.png 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-1-600x247.png 600w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-1.png 748w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>We can complete the top and bottom rows by dividing distance by the time.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-7350\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-2-300x123.png\" alt=\"short-table-2\" width=\"300\" height=\"123\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-2-300x123.png 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-2-600x245.png 600w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-2.png 748w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Next, we can complete the \u201ctime\u201d column.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-7351\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-3-300x127.png\" alt=\"short-table-3\" width=\"300\" height=\"127\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-3-300x127.png 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-3-600x254.png 600w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-3.png 746w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Finally, we can divide the length of the third leg, 48 kilometers, by the time for the third leg, 1 hour, to determine the rate for the third leg.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-7352\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-4-300x126.png\" alt=\"short-table-4\" width=\"300\" height=\"126\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-4-300x126.png 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-4-600x253.png 600w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/short-table-4.png 746w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If you haven&#8217;t been following our series on RTD tables, take a few minutes to catch up: Using Diagrams to Solve Rate Problems: Part 1 Using Diagrams to Solve Rate Problems: Part 2 A Different Use of the RTD Table: Part 1 A Different Use of the RTD Table: Part 2 Using the RTD Table [&hellip;]<\/p>\n","protected":false},"author":82,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[193],"tags":[],"ppma_author":[13222],"class_list":["post-5456","post","type-post","status-publish","format-standard","hentry","category-word-problems"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - 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He\u2019s earned multiple perfect scores on the GRE, GMAT, and LSAT. He\u2019d rather have perfect pitch or be able to run low 1:40s for the 800 meters, but you take what you get. He has decades of teaching and curriculum-development experience. One of these days he might finish his dissertation and collect that Ph.D. in philosophy. Might.","url":"https:\/\/magoosh.com\/gmat\/author\/michaelschwartz\/"}]}},"authors":[{"term_id":13222,"user_id":82,"is_guest":0,"slug":"michaelschwartz","display_name":"Michael Schwartz","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/d93dd6a3ce8134de72c26b5762ae2241005cd9e7537876e27dab68d9c44b2ae8?s=96&d=mm&r=g","user_url":"","last_name":"Schwartz","first_name":"Michael","description":"Michael Schwartz is really good at standardized tests. He\u2019s earned multiple perfect scores on the GRE, GMAT, and LSAT. He\u2019d rather have perfect pitch or be able to run low 1:40s for the 800 meters, but you take what you get. He has decades of teaching and curriculum-development experience. One of these days he might finish his dissertation and collect that Ph.D. in philosophy. Might."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/5456","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/82"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=5456"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/5456\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=5456"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=5456"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=5456"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=5456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}