{"id":5446,"date":"2015-01-12T09:00:12","date_gmt":"2015-01-12T17:00:12","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=5446"},"modified":"2020-01-15T10:48:21","modified_gmt":"2020-01-15T18:48:21","slug":"using-the-rtd-table-for-a-complicated-problem","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/","title":{"rendered":"Using the RTD Table for a Complicated Problem"},"content":{"rendered":"<p>My last few blog posts have involved rate problems about simultaneous movement. In each of these problems we discovered exactly two travelers who either (1) moved at their own constant rates for the entire time period covered by the story, or (2) moved at their own constant rates\u00a0 and started and stopped simultaneously.<\/p>\n<p>If you&#8217;d like to review before moving on, check out my previous posts on the topic:<\/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<\/ul>\n<p>We used the RTD (Rate, Time, and Distance) table to manage these problems, but some test-takers probably found that method to be overkill. Those readers judged that they could translate the problems directly from English to algebra without benefit of any table.<\/p>\n<p>Today I\u2019m going to give you a more complicated problem, one in which the travelers don\u2019t move simultaneously:<\/p>\n<p><em>Jan\u2019s house and Cindy\u2019s house are joined by a straight road 24 miles long. Jan and Cindy agree to meet at a restaurant along that road, twice as far from Jan\u2019s house as from Cindy\u2019s. Beginning at noon, Cindy walks to the restaurant at a constant speed of 3 miles per hour. Later, Jan drives to the restaurant at a constant speed of 30 miles per hour. If they arrive at the restaurant simultaneously, at what time did Jan begin her drive?<\/em><\/p>\n<p><em>A) 12:32<br \/>\n<\/em><em>B) 1:25<br \/>\n<\/em><em>C) 1:52<br \/>\n<\/em><em>D) 2:08<br \/>\n<\/em><em>E) 2:40<\/em><\/p>\n<p>This is likely to be a frustrating problem. The algebra\u2014if we can get to the algebra\u2014probably won\u2019t be too complicated, but the translation <em>into<\/em> algebra looks daunting, if only because we haven\u2019t likely seen a very close model of this problem before. Let\u2019s try our good friend the RTD table, and see if it eases the translation.<\/p>\n<p>We\u2019ll set the table up as we have before, with columns for rate, time, and distance, and with rows for Jan, Cindy, and their combined distance:<\/p>\n<p><center><a href=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-8.jpg\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-5476\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-8-300x225.jpg\" alt=\"Image 8\" width=\"300\" height=\"225\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-8-300x225.jpg 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-8-1024x768.jpg 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/center>With our earlier uses of the RTD table I circled the cell for whose value we were solving, but there is no such cell here. What cell corresponds to the time at which Jan began to drive? None. So let\u2019s note what we\u2019re solving for as well.<\/p>\n<p><center><a href=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-9.jpg\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-5477\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-9-300x225.jpg\" alt=\"Image 9\" width=\"300\" height=\"225\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-9-300x225.jpg 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-9-1024x768.jpg 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/center><\/p>\n<h2>Rates.<\/h2>\n<p>We\u2019re given Jan\u2019s and Cindy\u2019s rates directly, so let\u2019s put those in.<\/p>\n<p><center><a href=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-10.jpg\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-5478\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-10-300x225.jpg\" alt=\"Image 10\" width=\"300\" height=\"225\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-10-300x225.jpg 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-10-1024x768.jpg 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/center>Unlike our practice with simultaneous-movement problems, we can\u2019t add Jan\u2019s and Cindy\u2019s rates to get a combined rate. There is no combined rate that holds for the entire story. At first only Cindy is moving, so the combined rate is just her rate, 3 mph. Later, they\u2019re both moving, so the combined rate is the sum of their rates, 33 mph. There\u2019s no good way to use either of those \u201ccombined\u201d rates, so we\u2019ll cross out that cell.<\/p>\n<p><center><a href=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-11.jpg\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-5479\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-11-300x225.jpg\" alt=\"Image 11\" width=\"300\" height=\"225\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-11-300x225.jpg 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-11-1024x768.jpg 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/center>&nbsp;<\/p>\n<h2>Distance.<\/h2>\n<p>We are given the combined distances for Jan and Cindy, 24 miles, so we can include that.\u00a0 We\u2019re told that the restaurant is \u201ctwice as far from Jan\u2019s house as from Cindy\u2019s.\u201d If we call the distance from Cindy\u2019s house <em>d<\/em>, then the distance from Jan\u2019s house must be 2<em>d<\/em>.<\/p>\n<p><center><a href=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-12.jpg\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-5480\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-12-300x225.jpg\" alt=\"Image 12\" width=\"300\" height=\"225\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-12-300x225.jpg 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-12-1024x768.jpg 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/center>We can now make an equation from he distance column:<\/p>\n<p><em>d<\/em>+2<em>d<\/em>=24<\/p>\n<p>3<em>d<\/em>=24<\/p>\n<p><em>d<\/em>=8.<\/p>\n<p>So the restaurant is 8 miles from Cindy\u2019s house and 16 miles from Jan\u2019s.<\/p>\n<p><center><a href=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-13.jpg\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-5481\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-13-300x225.jpg\" alt=\"Image 13\" width=\"300\" height=\"225\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-13-300x225.jpg 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-13-1024x768.jpg 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/center>That\u2019s all the value that you\u2019re going to get from the bottom row. If you saw right away that \u201ctwice as far from Jan\u2019s house as from Cindy\u2019s\u201d means 16 miles from Jan\u2019s house and 8 miles from Cindy\u2019s, then the bottom row added no value for you. That\u2019s alright, though; it just takes a second to add.<\/p>\n<p>&nbsp;<\/p>\n<h2>Time.<\/h2>\n<p>Let\u2019s complete the rows for Cindy and Jan. Since we know that Cindy\u2019s rate is 3 mph and that her distance is 8 miles, we can conclude that her time was 8\/3 hours. Since we know that Jan\u2019s rate is 30 mph and that her distance is 16 miles, we can conclude that her time was 16\/30 hours.<\/p>\n<p><center><a href=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-141.jpg\"><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-141-300x225.jpg\" alt=\"Image 14\" width=\"300\" height=\"225\" class=\"alignnone size-medium wp-image-5483\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-141-300x225.jpg 300w, https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-141-1024x768.jpg 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/center><\/p>\n<p>But now what? Well, if Cindy took 8\/3 of an hour, then she took \u00a0hours, or 2 hours and 40 minutes. Since she started at noon, she arrived at the restaurant at 2:40.<\/p>\n<p>Since Cindy and Jan arrived simultaneously, Jan too arrived at 2:40. At what time did she leave? Well, she took 16\/30 of an hour. That\u2019s 32\/60, or 32 minutes. Since she arrived at 2:40 after 32 minutes of travel, she must have started her drive at 2:08.<\/p>\n<p>&nbsp;<\/p>\n<h2>Could we do this without the RTD table?<\/h2>\n<p>If you\u2019ve read my other blogs on the use of this table, then you know that the answer is \u201cyes,\u201d at least for some people. The table is an aid to translation, and a few people are able to translate even very complicated rate problems directly into algebra without benefit of the table.<\/p>\n<p>Still, I think that the RTD table is especially useful for this problem, even though as we used it here it turned out to just be two equations stacked one on the other, and even though it left us with a fair bit of work still to do. Disciplined well-practiced use of the RTD table allows us to chip away at the familiar parts of the problem and to reserve our cognitive resources for the less familiar parts.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>My last few blog posts have involved rate problems about simultaneous movement. In each of these problems we discovered exactly two travelers who either (1) moved at their own constant rates for the entire time period covered by the story, or (2) moved at their own constant rates\u00a0 and started and stopped simultaneously. If you&#8217;d [&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-5446","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) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Using the RTD Table for a Complicated Problem - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Using the RTD Table for a Complicated Problem\" \/>\n<meta property=\"og:description\" content=\"My last few blog posts have involved rate problems about simultaneous movement. 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If you&#8217;d [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GMAT\u00ae Exam\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/MagooshGMAT\/\" \/>\n<meta property=\"article:published_time\" content=\"2015-01-12T17:00:12+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-01-15T18:48:21+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/Image-8-300x225.jpg\" \/>\n<meta name=\"author\" content=\"Michael Schwartz\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Michael Schwartz\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/\"},\"author\":{\"name\":\"Michael Schwartz\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/95a95e68f2ccbf70a6bacf5a260eaacf\"},\"headline\":\"Using the RTD Table for a Complicated Problem\",\"datePublished\":\"2015-01-12T17:00:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/\"},\"wordCount\":909,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"articleSection\":[\"GMAT Word Problems\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/\",\"name\":\"Using the RTD Table for a Complicated Problem - Magoosh Blog \u2014 GMAT\u00ae Exam\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\"},\"datePublished\":\"2015-01-12T17:00:12+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/gmat\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Using the RTD Table for a Complicated Problem\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"name\":\"Magoosh Blog \u2014 GMAT\u00ae Exam\",\"description\":\"Everything you need to know about the GMAT\",\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/magoosh.com\/gmat\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\",\"name\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"contentUrl\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"width\":265,\"height\":60,\"caption\":\"Magoosh\"},\"image\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/MagooshGMAT\/\",\"https:\/\/twitter.com\/MagooshGMAT\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/95a95e68f2ccbf70a6bacf5a260eaacf\",\"name\":\"Michael Schwartz\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/image\/e394ca0b8f7a8ce5d11ab69a2756a9cf\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/d93dd6a3ce8134de72c26b5762ae2241005cd9e7537876e27dab68d9c44b2ae8?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/d93dd6a3ce8134de72c26b5762ae2241005cd9e7537876e27dab68d9c44b2ae8?s=96&d=mm&r=g\",\"caption\":\"Michael Schwartz\"},\"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.\",\"url\":\"https:\/\/magoosh.com\/gmat\/author\/michaelschwartz\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Using the RTD Table for a Complicated Problem - Magoosh Blog \u2014 GMAT\u00ae Exam","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/magoosh.com\/gmat\/using-the-rtd-table-for-a-complicated-problem\/","og_locale":"en_US","og_type":"article","og_title":"Using the RTD Table for a Complicated Problem","og_description":"My last few blog posts have involved rate problems about simultaneous movement. In each of these problems we discovered exactly two travelers who either (1) moved at their own constant rates for the entire time period covered by the story, or (2) moved at their own constant rates\u00a0 and started and stopped simultaneously. 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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\/5446","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=5446"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/5446\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=5446"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=5446"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=5446"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=5446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}