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Buy "All-In-One Standard ($149)", get free Daily quiz (2 mon). Coupon code : SPECIAL # Math Revolution and GMAT Club Contest! John drove on a highway at a  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 05 Jun 2013 Posts: 35 Re: Math Revolution and GMAT Club Contest! John drove on a highway at a [#permalink] ### Show Tags 19 Dec 2015, 02:30 1 Lets assume r (Speed ) to be multiple of 3, say 30 r=30(Since 4r/3 has 3 in denominator). r=30 miles, 4r/3= 40 miles John's Speed = 30 miles. Tom's Speed= 40 miles Let t be time that Tom has travelled to catch with John and therefore John would have travelled for (t+2) hrs When Tom caught up John, the distance travelled would be the same. Equating distance on both sides 30(t+2) = 40t 30t+60=40t t=6hrs Time travelled by Tom to catch up with John = 6hrs, which is 40*6= 240 miles, which is 8r, since we assumed r as 30miles/hr. Therefore answer is C, 8r. Moderator Joined: 21 Jun 2014 Posts: 1113 Location: India Concentration: General Management, Technology GMAT 1: 540 Q45 V20 GPA: 2.49 WE: Information Technology (Computer Software) Re: Math Revolution and GMAT Club Contest! John drove on a highway at a [#permalink] ### Show Tags 19 Dec 2015, 02:56 1 Let's say Tom Cought up with john in x hours. As John started 2 hours before tom, So in (x + 2) hours john traveled = (x + 2)*r = rx + 2r miles In x hrs Tom traveled = (4r/3)*x = 4rx/3 miles we can equate the distances covered (same distance - from starting point till meeting point), Hence: 4rx/3 = rx + 2r, 4rx = 3rx + 6r , rx = 6r , x = 6 hours. John covered = rx + 2r = 6r + 2r = 8r miles. Option C is the correct answer. _________________ --------------------------------------------------------------- Target - 720-740 Project PS Butler - https://gmatclub.com/forum/project-ps-butler-practice-everyday-280904.html http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html Manager Joined: 10 Aug 2015 Posts: 54 Concentration: General Management, Entrepreneurship GMAT 1: 730 Q48 V42 Re: Math Revolution and GMAT Club Contest! John drove on a highway at a [#permalink] ### Show Tags 19 Dec 2015, 13:56 1 The key thing to understand here is that when Tom catches up with John, they have covered the same distance. What the question really asks for is this distance, which is expressed as $$T * R$$ in the answer choices. So our goal is to express the distance covered by John and Tom with rate and time. Distance covered by John : $$2 * r$$(distance covered during the first 2 hours at r miles) We define a new variable, $$T$$ = the time it took John to travel the second portion of the trip. The distance he covers is $$r * T$$. Total distance covered by John: $$2r + rT$$. Distance covered by Tom : Tom travels at a speed of $$\frac{4}{3}r$$. The total travel time of Tom is equal to the time it takes John to travel the second part of his trip --> $$T$$. Total distance covered by Tom: $$\frac{4}{3}rT$$ Since John and Tom have covered the same distance when they meet up, we can solve the following equation for T : $$2r + rT = \frac{4}{3}rT$$ $$2r = \frac{1}{3}rT$$ $$T = 6$$. So it took Tom 6 hours to catch up with John. And the distance covered is : $$\frac{4}{3}r * 6 = 8r$$ Answer C. Math Expert Joined: 02 Sep 2009 Posts: 52938 Re: Math Revolution and GMAT Club Contest! John drove on a highway at a [#permalink] ### Show Tags 20 Dec 2015, 09:51 Bunuel wrote: Math Revolution and GMAT Club Contest Starts! QUESTION #12: John drove on a highway at a constant speed of r miles per hour in 13:00. Then, 2 hours later, Tom drove on the same highway at a constant speed of 4r/3 miles per hour in 15:00. If both drivers maintained their speed, how many did John drive on a highway, in miles, when Tom caught up with John? A. 3r B. 5r C. 8r D. 9r E. 10r Check conditions below: Math Revolution and GMAT Club Contest The Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth$299!

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MATH REVOLUTION OFFICIAL SOLUTION:

It is important to note that in speed problems, time passes at the same time.

John traveled 2r miles during the first 2 hours and he traveled rt miles during the next t hours. In case of Tom, he traveled 4rt/3 miles during t hours. The distances they traveled are rt and 4rt/3, respectively,instead of rt1 and 4rt2/3,respectively because both traveled during the same time period. Then, $$2r+rt=\frac{4rt}{3}$$ → $$2+t=\frac{4t}{3}$$ → t=6. This means that Tom caught up with John after John traveled 6 hours. So we can solve 2r+6r=8r, and the correct answer is C.

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Re: Math Revolution and GMAT Club Contest! John drove on a highway at a  [#permalink]

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Re: Math Revolution and GMAT Club Contest! John drove on a highway at a   [#permalink] 09 Oct 2018, 09:33

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