{"id":5436,"date":"2015-01-08T09:00:18","date_gmt":"2015-01-08T17:00:18","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=5436"},"modified":"2020-01-15T10:48:22","modified_gmt":"2020-01-15T18:48:22","slug":"a-different-use-of-the-rtd-table-part-2","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/","title":{"rendered":"A Different Use of the RTD Table: Part 2"},"content":{"rendered":"

Let\u2019s recap where we left off yesterday<\/a>.\u00a0 We were working with this diagram:<\/p>\n

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

We wanted to solve for Mary\u2019s time, t<\/em>.<\/p>\n

In every row the relationship among rate, time, and distance is the same: RT=D. In this diagram the bottom row looks the most promising, since it alone contains only the variable for which we\u2019re solving. (Why mess around with d<\/em> if we don\u2019t need to?) So let\u2019s look at the equation implicit in that bottom row:<\/p>\n

\"aduotrtfadsottpp2_img1\"<\/a><\/p>\n

Cross-multiplying to get the difference between those fractions yields:<\/p>\n

\"aduotrtfadsottpp2_img2\"<\/a><\/p>\n

or:<\/p>\n

\"aduotrtfadsottpp2_img3\"<\/a><\/p>\n

Could I have made the table simpler?<\/h2>\n

Yes. I wanted to show an efficient use of the table, but I didn\u2019t want to insist on the optimal use.<\/p>\n

You could, for instance, have represented Mary\u2019s rate as 200 rather than as 1000\/5, and Kate\u2019s rate as 500\/3 rather than as 1000\/6.\u00a0 Doing that in the diagram or simplifying the moment you\u2019d pull the equation out of the diagram would have yielded\u00a0\"aduotrtfadsottpp2_img4\"\u00a0instead of\u00a0\"aduotrtfadsottpp2_img5\"<\/a>\u00a0That would have allowed you to multiply through by 3 rather than to cross-multiply:<\/p>\n

\"aduotrtfadsottpp2_img6\"<\/a><\/p>\n

That definitely saves some time and effort, but if our first, efficient-but-not-optimal use of the table comes more easily, that\u2019s OK. Sometimes there\u2019s a little trade-off between the ease of translation (English-into-algebra) and the ease of solution (algebraic manipulation).<\/p>\n

By the way, I wouldn\u2019t take it a step further and represent Kate\u2019s rate as . Mixed numbers are usually more difficult to clear than are improper fractions.<\/p>\n

 <\/p>\n

But some uses of the RTD table are really<\/em> inefficient!<\/h2>\n

For instance, many people build RTD tables with no bottom row for the sum or the difference of the rates and distances. This is just inviting complexity and computational error. Such a table often yields a system of two equations and two variables rather than a single equation with a single variable.<\/p>\n

Consider what our table would have looked like with no bottom roappw:<\/p>\n

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

This would have yielded a system of equations:<\/p>\n

\"aduotrtfadsottpp2_img7\"<\/a><\/p>\n

If you distribute those fractions right away you\u2019re in for a lot of work. It might occur to you to instead isolate t <\/em>in each equation, then to solve for d<\/em>, and finally to solve for t<\/em>. It turns out that that, too, is a lot of work:<\/p>\n

\"aduotrtfadsottpp2_img8\"<\/a><\/p>\n

But 3750 isn\u2019t one of our answers! That\u2019s because we\u2019re solving for t<\/em> rather than for d. <\/em>We have to return to one of our equations that related t<\/em> to d<\/em>, substitute 3750 for d<\/em>, and solve for t<\/em>:<\/p>\n

\"aduotrtfadsottpp2_img9\"<\/a><\/p>\n

Bottom-line? Always include an extra row for simultaneous-movement problems. You won\u2019t need to use it every time, but it will you save you a lot of trouble when you do need it. <\/em><\/p>\n

Hey, I think that I could answer this problem without the table!<\/strong><\/p>\n

Well, then you probably could.<\/p>\n

You might remember this formula from my earlier post on the RTD table: (combined rate)(time)=(combined distance). We used that for travelers moving simultaneously in opposite directions.<\/p>\n

Here\u2019s a similar, and similarly simple, formula for travelers moving simultaneously in the same<\/em> direction: (difference in rates)(time)=(difference in distances).* Applying that formula to this problem directly yields our equation:\u00a0
\n\"aduotrtfadsottpp2_img1\"<\/a> <\/p>\n

You\u2019ve still got to do the math, of course.<\/p>\n

*In fact, some people point out that the second formula is just a special case of the first, since subtraction is one way to combine values. I find that confusing, since for non-mathematicians like us \u201ccombined\u201d usually means \u201cadded.\u201d<\/p>\n

 <\/p>\n

Next time, a really hard rate problem.<\/h2>\n

Just in case you\u2019ve patiently read these posts on the RTD table and you still<\/em> haven\u2019t seen a problem that you couldn\u2019t translate directly from English to Algebra, my next post will feature a more complicated rate problem.<\/p>\n

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

Let\u2019s recap where we left off yesterday.\u00a0 We were working with this diagram: We wanted to solve for Mary\u2019s time, t. In every row the relationship among rate, time, and distance is the same: RT=D. In this diagram the bottom row looks the most promising, since it alone contains only the variable for which we\u2019re […]<\/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-5436","post","type-post","status-publish","format-standard","hentry","category-word-problems"],"acf":[],"yoast_head":"\nA Different Use of the RTD Table: Part 2 - 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-2\/\" \/>\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 2\" \/>\n<meta property=\"og:description\" content=\"Let\u2019s recap where we left off yesterday.\u00a0 We were working with this diagram: We wanted to solve for Mary\u2019s time, t. In every row the relationship among rate, time, and distance is the same: RT=D. In this diagram the bottom row looks the most promising, since it alone contains only the variable for which we\u2019re […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/\" \/>\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=\"2015-01-08T17:00:18+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\/Image-6-300x225.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\/a-different-use-of-the-rtd-table-part-2\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/\"},\"author\":{\"name\":\"Michael Schwartz\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/95a95e68f2ccbf70a6bacf5a260eaacf\"},\"headline\":\"A Different Use of the RTD Table: Part 2\",\"datePublished\":\"2015-01-08T17:00:18+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/\"},\"wordCount\":639,\"commentCount\":0,\"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-2\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/\",\"name\":\"A Different Use of the RTD Table: Part 2 - Magoosh Blog \u2014 GMAT\u00ae Exam\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\"},\"datePublished\":\"2015-01-08T17:00:18+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/gmat\/a-different-use-of-the-rtd-table-part-2\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/gmat\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"A Different Use of the RTD Table: Part 2\"}]},{\"@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. 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