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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Noelle walks from point A to point B at an average speed of ##### This topic has 4 expert replies and 0 member replies ### Top Member ## Noelle walks from point A to point B at an average speed of ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour? A. 6.75 B. 7 C. 7.25 D. 7.5 E. 7.75 OA D Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour? A. 6.75 B. 7 C. 7.25 D. 7.5 E. 7.75 For these kinds of questions, I typically follow the approach that Fabio used (assign a nice value to the distance). But we can also solve the question algebraically: Let d = the distance between Points A and B. Let x = the Noelle's speed from Point B to Point A. We want the average speed for the entire trip to be 6 kilometers per hour. So, we want: (TOTAL distance)/(TOTAL travel time) = 6 kmh In other words: (TOTAL distance)/(travel time from A to B + travel time from B to A) = 6 kmh Travel time = distance/speed So, we get: (d + d)/(d/5 + d/x) = 6 kmh Simplify to get: (2d)/(d/5 + d/x) = 6 Rewrite fractions with same denominator: (2d)/(dx/5x + 5d/5x) = 6 Combine fractions: (2d)/[(dx + 5d)/5x] = 6 Simplify: (2d)(5x)/(dx + 5d) = 6 Simplify: 10dx/[d(x + 5)] = 6 Divide top and bottom by d to get: 10x/(x + 5) = 6 Multiply both sides by (x+5) to get: 10x = 6(x + 5) Expand: 10x = 6x + 30 So: 4x = 30 x = 30/4 = 7.5 Answer: D Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour? A. 6.75 B. 7 C. 7.25 D. 7.5 E. 7.75 We can let the distance from point A to point B = d, so the entire trip is 2d. Thus, the time to go from point A to point B is d/5. If we let r = Noelleâ€™s walking rate from point B to point A, then her time is d/r. We can plug all of our values into the average rate formula: average rate = (distance 1 + distance 2)/(time 1 + time 2) 6 = 2d/(d/5 + d/r) 6(d/5 + d/r) = 2d 6d/5 + 6d/r = 2d 6/5 + 6/r = 2 6/r = 4/5 30 = 4r 7.5 = r Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorDC wrote: Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour? A. 6.75 B. 7 C. 7.25 D. 7.5 E. 7.75 Source: Magoosh $$\left. \matrix{ {V_{A \to B}} =\,\, 5\,\,{{{\rm{km}}} \over {\rm{h}}} \hfill \cr {V_{B \to A}} =\,\, ?\,\,{{{\rm{km}}} \over {\rm{h}}}\,\, \hfill \cr} \right\}\,\,\,{\rm{for}}\,\,{V_{{\rm{average}}}} = 6\,\,{{{\rm{km}}} \over {\rm{h}}}$$ $${\rm{Take}}\,\,{\rm{dist}}\left( {A,B} \right) = 30\,\,{\rm{km}}$$ LetÂ´s use UNITS CONTROL, one of the most powerful tools of our method! $$\left. \matrix{ A \to B\,\,\,:\,\,\,{\rm{30}}\,\,{\rm{km}}\left( {{{1\,\,{\rm{h}}} \over {5\,\,{\rm{km}}}}} \right) = 6\,\,{\rm{h}} \hfill \cr A \to B \to A\,\,\,:\,\,\,2 \cdot {\rm{30}}\,\,{\rm{km}}\left( {{{1\,\,{\rm{h}}} \over {6\,\,{\rm{km}}}}} \right) = 10\,\,{\rm{h}}\,\,\,\, \hfill \cr} \right\}\,\,\,\, \Rightarrow \,\,\,\,B \to A = 10 - 6 = 4\,\,{\rm{h}}$$ $$? = {{30} \over 4} = {{28 + 2} \over 4} = 7{1 \over 2}\,\,\,\,\,\,\left[ {{{{\rm{km}}} \over {\rm{h}}}} \right]$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour? A. 6.75 B. 7 C. 7.25 D. 7.5 E. 7.75 Let the distance between A and B = the LCM of the two speeds = 5*6 = 30 kilometers, implying that the distance for the entire round trip = 60 kilometers. At a rate of 5 kph, the time to travel the 30 kilometers from A to B = d/r = 30/5 = 6 hours. At a rate of 6 kph, the time to travel the entire 60-kilometer round trip = d/r = 60/6 = 10 hours. Time to travel from B to A = (time for the entire round trip) - (time to travel from A to B) = 10-6 = 4 hours. Since it takes 4 hours to travel the 30 kilometers from B to A, the rate from B to A = d/t = 30/4 = 7.5 kph. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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