{"id":2415,"date":"2016-08-31T10:32:26","date_gmt":"2016-08-31T15:32:26","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=2415"},"modified":"2020-09-11T20:42:54","modified_gmt":"2020-09-11T20:42:54","slug":"gre-quantitative-rates-and-work-question-practice","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/gre\/gre-quantitative-rates-and-work-question-practice\/","title":{"rendered":"GRE Quantitative: Rates and Work Question Practice"},"content":{"rendered":"<p>On the GRE, Rates and Work questions may appear in any of the Quantitative question formats: Multiple Choice, Numeric Entry, or Quantitative Comparisons. A \u201crate\u201d is anything\u00a0<em>per<\/em>\u00a0anything (miles per hour, laps per minute, gallons of paint per square inch of wall, etc.).<br \/>\nIn the meantime, here are two formulas you should memorize to get these types of questions correct on your GRE test:<\/p>\n<ul>\n<li>The first GRE formula to memorize before your GRE test is: D = R x T. This stands for Distance = Rate x Time. It can also be rearranged as Time = Distance \/ Rate or as Rate = Distance \/ Time.<\/li>\n<li>The second formula you\u2019ll want to know is: Average Rate = Total Distance \/ Total Time. Average Rate may have the word \u201caverage\u201d in it, but remember that this is an entirely different concept from mathematical mean. Let\u2019s look at an example question:<\/li>\n<\/ul>\n<p>Let&#8217;s review some practice questions:<br \/>\n&nbsp;<br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-0  el_before_av_promobox  avia-builder-el-first  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >GRE Quantitative: Rates and Work Practice Question<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n\t<div  style='background:#ffffff;color:#444444;border-color:#444444;' class='av_promobox  avia-button-no   avia-builder-el-1  el_after_av_heading  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n1. Joanne drove 80 miles to see her mother. It took her 4 hours to get there. Then, she left her mother\u2019s and drove another 40 miles to visit her aunt, but this time went 40mph. What was her average speed for the whole trip?<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-2  el_after_av_promobox  el_before_av_hr \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-1\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-1\">Explanation<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-1\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p>Remember Average Speed = Total Distance \/ Total Time.<br \/>\nJoanne traveled 80 miles + 40 miles so the Total Distance was 120 miles. She drove for 4 hours + 1 hour (since 40 miles at 40mph would only be 1 hour) so the Total Time was 5 hours. 120\/5 = 24.<br \/>\nTherefore,<strong>\u00a0the average speed for the whole trip was 24 mph<\/strong>. Think of Average Speed as a weighted average. Joanne spent more time going 20mph than 40mph, so it makes sense that the Average Speed would be closer to 20mph.<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n<div   class='hr hr-short hr-center   avia-builder-el-3  el_after_av_toggle_container  el_before_av_promobox '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\nLet\u2019s try another practice question.<br \/>\n\t<div  style='background:#ffffff;color:#444444;border-color:#444444;' class='av_promobox  avia-button-no   avia-builder-el-4  el_after_av_hr  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n2. Marion spent a day on a sightseeing trip in Tuscany. First she boarded a bus which went 15mph through a 30 mile section of the countryside. The bus then stopped for lunch in Florence before continuing on a 3 hour tour of the city&#8217;s sights at speed of 10mph. Finally, the bus left the city and drove 40 miles straight back to the hotel. Marion arrived back at her hotel exactly 2 hours after leaving Florence. What was the bus&#8217;s average rate for the entire journey?<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-5  el_after_av_promobox  el_before_av_hr \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-2\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-2\">Explanation<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-2\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p>To find the &#8220;Average Rate&#8221; of the bus, we know we will need to find the Total Distance and the Total Time, so let&#8217;s see how we can use the D = R x T formula to find the missing info.<br \/>\nFor the first part of the trip, we know that 30 miles = 15mph x T, so we know that T = 2 hours.<br \/>\nFor the middle part of the trip, we know that D = 10mph x 3 hours, so we know that D = 30 miles.<br \/>\nFor the last part of the trip, we know that 40 miles = R x 2 hours, so we know that R = 20mph.<br \/>\nNow we can find the Total Distance and the Total Time.<br \/>\nTotal Distance = 30 miles + 30 miles + 40miles = 100 miles.<br \/>\nTotal Time = 2 hours + 3 hours + 2 hours = 7 hours.<br \/>\nSo\u00a0<strong>the Average Rate = 100 miles\/ 7 hours = 14.28mph.<\/strong><\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n<div   class='hr hr-short hr-center   avia-builder-el-6  el_after_av_toggle_container  el_before_av_heading '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-7  el_after_av_hr  el_before_av_promobox  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Converting Rates on the GRE<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nSome\u00a0GRE\u00a0rate questions will be presented as Quantitative Comparisons and will require conversions. You won\u2019t be required to know complicated conversions (such as liters to gallons) but you must know a few basics chronological ones. There are 60 seconds in 1 minute, 60 minutes in 1 hour, 24 hours in a day, and 365 days in one year. For measurement, it\u2019s enough to know that a foot has 12 inches.<br \/>\nLet\u2019s look at this\u00a0question:<br \/>\n\t<div  style='background:#ffffff;color:#444444;border-color:#444444;' class='av_promobox  avia-button-no   avia-builder-el-8  el_after_av_heading  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n3.<\/p>\n<table>\n<tbody>\n<tr>\n<th>Column A<\/th>\n<th>Column B<\/th>\n<\/tr>\n<tr>\n<td>The number of seconds in 2 hours<\/td>\n<td>The number of days in 20 years<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A. Quantity A is greater.<br \/>\nB. Quantity B is greater.<br \/>\nC. The two quantities are equal.<br \/>\nD. The relationship cannot be determined from the information given.<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-9  el_after_av_promobox  el_before_av_hr \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-3\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-3\">Explanation<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-3\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p>2 hours = 120 minutes = 7200 seconds<br \/>\n20 years\u00a0 = 365 days x 20 = 7300.<br \/>\n<strong>Even without considering leap years, (B) will be greater.<\/strong><\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n<div   class='hr hr-short hr-center   avia-builder-el-10  el_after_av_toggle_container  el_before_av_promobox '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\nSometimes the\u00a0GRE\u00a0will present a work problem involving the amount of work that can be done individually, and then combined. Remember that the amount of a job that an individual can complete in one hours is always the reciprocal of the number of hours it takes to complete the full job.<br \/>\nFor example, if Sheila takes 4 hours to clean her room, then she can clean \u00bc of her room in 1 hour. If Sheila\u2019s mom can clean her room in 3 hours, then Sheila\u2019s mom can clean 1\/3 of the room in 1 hour. Working together, they will clean \u00bc + 1\/3 = 7\/12 of the room in 1 hour. As a result, it will take them less than 2 hours to finish cleaning when they work together. Remember to ADD the individual rates to find the COMBINED rate. Let\u2019s try one more word problem to put our formulas to the test!<br \/>\n\t<div  style='background:#ffffff;color:#444444;border-color:#333333;' class='av_promobox  avia-button-no   avia-builder-el-11  el_after_av_hr  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n4. Tracey ran to the top of a steep hill at an average pace of 6 miles per hour. She took the exact same trail back down. To her relief, the descent was much faster; her average speed rose to 14 miles per hour. If the entire run took Tracey exactly one hour to complete and she did not make any stops, how many miles is the trail one way?<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-12  el_after_av_promobox  avia-builder-el-last \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-4\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-4\">Explanation<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-4\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p>For the way up the hill, we know that D = 6mph x T.<br \/>\nFor the way down the hill, we know that D = 14mph x T.<br \/>\nSince we went know that the distance up the hill was the same as the distance down the hill, we can pick a number for D. Let&#8217;s choose &#8220;84&#8221; since it is a multiple of both 6 and 14. \u00a0If 84 = 6mph x T, then we know that T = 14 hours. If 84 = 14mph x T, then we know that T\u00a0 = 6 hours.<br \/>\nNow we can use another formula, the Average Rate formula, to find the average speed for the WHOLE trip.\u00a0Average Rate = Total Distance \/ Total Time<br \/>\nUsing our Picked Number of 84, we know that the Total Distance traveled would be 168 miles. The Total Time is 14 hours + 6 hours = 20 hours. \u00a0So the Average Rate = 168 miles \/ 20 hours = 8.4 mph.<br \/>\nIt doesn&#8217;t matter that Tracey didn&#8217;t &#8220;really&#8221; go 168 miles, or that we know she didn&#8217;t &#8220;really&#8221; go 20 hours. We Picked a Number just so that we could find the ratio of the Total Distance to the Total Time in order to calculate the Average Rate of the ENTIRE journey.<br \/>\nNow that we have found the Average Rate for the whole trip, we can plug it in to the &#8220;DIRT&#8221; formula to find the ACTUAL distance for the entire journey.<br \/>\nD = R x T<br \/>\nD = 8.4mph x 1 hour<br \/>\nWe know that T = 1 hour because the problem told us so. Therefore, the actual distance for the entire trip was 8.4 miles. The problem asks how many miles the trail was one way. 8.4 \/ 2 = 4.2. The answer to the question is 4.2 miles.<br \/>\nYou could also solve this problem in other ways, including using a system of equations and substitution, but it&#8217;s nice to know that you can pick a number for the Distance traveled and use it to find the Average Rate for the whole journey!<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>On the GRE, Rates and Work questions may appear in any of the Quantitative question formats: Multiple Choice, Numeric Entry, or Quantitative Comparisons. A \u201crate\u201d is anything\u00a0per\u00a0anything (miles per hour, laps per minute, gallons of paint per square inch of wall, etc.). In the meantime, here are two formulas you should memorize to get these [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28926,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[68],"tags":[],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2415"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=2415"}],"version-history":[{"count":3,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2415\/revisions"}],"predecessor-version":[{"id":36364,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2415\/revisions\/36364"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/28926"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=2415"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=2415"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=2415"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}