{"id":5434,"date":"2015-01-07T09:00:27","date_gmt":"2015-01-07T17:00:27","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=5434"},"modified":"2020-01-15T10:48:22","modified_gmt":"2020-01-15T18:48:22","slug":"a-different-use-of-the-rtd-table-part-1","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-1\/","title":{"rendered":"A Different Use of the RTD Table: Part 1"},"content":{"rendered":"

In my last couple of posts (Using Diagrams to Solve GMAT Rate Problems Part 1<\/a> and Part 2<\/a>) I used a Rate-Time-Distance table, (or RTD table) to solve the most common sort of rate problem: a combined-rate problem in which two travelers move in opposite directions simultaneously. \u00a0(If you haven\u2019t read those posts and aren\u2019t otherwise familiar with the RTD table, then read them now.\u00a0This post will assume familiarity with the table.)<\/p>\n

Today and tomorrow we\u2019re going to use the table just a tiny bit differently to solve another common sort of rate problem, one in which two travelers move in the same direction<\/em> simultaneously.\u00a0 We\u2019ll set up the table today and use it to solve the problem tomorrow.<\/p>\n

Many problems in which two travelers move in the same direction<\/em> simultaneously involve a faster traveler starting behind a slower traveler, and catching up to or passing him.<\/p>\n

Mary and Kate are running clockwise around a circular track with a circumference of 500 meters, each at her own constant speed. Mary runs 1000 meters every five minutes and Kate runs 1000 meters every six minutes. \u00a0If Mary and Kate start opposite one another on the circular track, how many minutes must Mary run in order to pass Kate and catch her again?<\/em><\/p>\n

\"aduotrtfadsottp_img1\"<\/a><\/p>\n

The table looks a lot like those we\u2019ve seen before.<\/h2>\n

We\u2019ll begin with our familiar layout: three columns (for rate, time, and distance) and three rows (for Mary, Kate, and the difference between them). A lot of people mark the bottom row in such a table as \u201cC,\u201d for \u201ccombined,\u201d just as they would if Mary and Kate were traveling in opposite directions, though \u201ccombined\u201d in this case doesn\u2019t mean \u201cadded together.\u201d Just to be clear, I\u2019m going to label that bottom row with a delta, to remind myself to determine the difference between Mary\u2019s and Kate\u2019s rates and distances. I\u2019m also going to circle the cell representing Mary\u2019s time, since that\u2019s what we\u2019re solving for.<\/p>\n

\"Image<\/a><\/center><\/p>\n

 <\/p>\n

This is a good time to make and learn from mistakes!<\/h2>\n

Before we talk about how best to manage this problem and table, go ahead and copy the table above, then add the information from the problem.<\/p>\n

 <\/p>\n

How best to use the table here.<\/h2>\n

Now let\u2019s add the information that we\u2019ve been given.\u00a0 Begin with the rates. Mary\u2019s rate is not<\/em> 5 minutes and Kate\u2019s rate is not<\/em>\u00a0 6 minutes. Speeds are always D\/T, so Mary\u2019s and Kate\u2019s rates are 1000\/5 and 1000\/6 respectively.<\/p>\n

\"Image<\/a><\/center><\/p>\n

Similarly, Mary\u2019s time and distance are not<\/em> 5 minutes and 1000 meters, and Kate\u2019s time and distance are not<\/em> 6 minutes and 1000 meters. Those figures are given to you only to determine Mary\u2019s and Kate\u2019s rates. NEVER ASSUME THAT THE TIME AND DISTANCE THAT FIX THE RATE ARE THE APPROPRIATE FIGURES FOR THE TIME AND DISTANCE COLUMNS!<\/em><\/p>\n

In fact, Mary\u2019s and Kate\u2019s distances are so far unknown to us. Let\u2019s represent them with variables. Or better, let\u2019s represent them with a single<\/em> variable, using d<\/em> for Kate\u2019s distance. If Kate ran d<\/em> meters, how far would Mary run? Well, she\u2019d have to run an additional 250 meters to catch Kate, and then an additional 500 meters to lap her. That means that if Kate\u2019s distance were d<\/em> meters, Mary\u2019s distance would be d<\/em>+750 meters.<\/p>\n

\"Image<\/a><\/center><\/p>\n

Since Kate and Mary run simultaneously, a single time t<\/em> will suffice for all three rows.<\/p>\n

\"Image<\/a><\/center><\/p>\n

Finally, subtract <\/em>Kate\u2019s rate and distance from Mary\u2019s to fill in the bottom row.<\/p>\n

\"Image<\/a><\/center><\/p>\n

 <\/p>\n

Return tomorrow for a solution!<\/h2>\n

As we saw in our earlier posts on the RTD table, diagrams generally produce equations which we then solve algebraically. Diagrams are usually tools to help us translate word problems into algebra; they are not usually substitutes for manipulating equations.<\/p>\n

What equation can you draw from this table that would allow you to solve for t<\/em>?<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

In my last couple of posts (Using Diagrams to Solve GMAT Rate Problems Part 1 and Part 2) I used a Rate-Time-Distance table, (or RTD table) to solve the most common sort of rate problem: a combined-rate problem in which two travelers move in opposite directions simultaneously. \u00a0(If you haven\u2019t read those posts and aren\u2019t […]<\/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-5434","post","type-post","status-publish","format-standard","hentry","category-word-problems"],"acf":[],"yoast_head":"\nA Different Use of the RTD Table: Part 1 - 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\/a-different-use-of-the-rtd-table-part-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A Different Use of the RTD Table: Part 1\" \/>\n<meta property=\"og:description\" content=\"In my last couple of posts (Using Diagrams to Solve GMAT Rate Problems Part 1 and Part 2) I used a Rate-Time-Distance table, (or RTD table) to solve the most common sort of rate problem: a combined-rate problem in which two travelers move in opposite directions simultaneously. \u00a0(If you haven\u2019t read those posts and aren\u2019t […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-1\/\" \/>\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=\"2015-01-07T17:00:27+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-01-15T18:48:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gmat\/files\/2015\/01\/aduotrtfadsottp_img1.png\" \/>\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=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-1\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-1\/\"},\"author\":{\"name\":\"Michael Schwartz\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/95a95e68f2ccbf70a6bacf5a260eaacf\"},\"headline\":\"A Different Use of the RTD Table: Part 1\",\"datePublished\":\"2015-01-07T17:00:27+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-1\/\"},\"wordCount\":670,\"commentCount\":4,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"articleSection\":[\"GMAT Word Problems\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-1\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-1\/\",\"name\":\"A Different Use of the RTD Table: Part 1 - 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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. 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