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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 ## A hiker walking at a constant rate of 4 miles per hour is tagged by: BTGmoderatorLU ##### This topic has 4 expert replies and 0 member replies ### Top Member ## A hiker walking at a constant rate of 4 miles per hour is ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: GMAT Prep A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up? A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 The OA is C. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1434 messages Followed by: 31 members Upvotes: 59 Top Reply Quote: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. Five minutes after the passing the cyclist stops, while the hiker continues to walk at the hiker´s rate. How many minutes must the cyclist wait until the hiker catches up? A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 $$?\,\,\,:\,\,\,{\text{minutes}}\,\,\,\left( {{\text{last}}\,\,{\text{diagram}}} \right)$$ Let´s use UNITS CONTROL, one of the most powerful tools of our method! $${\rm{cyclist}}:\,\,\,5\min \,\,\left( {{{20\,\,{\rm{miles}}} \over {60\,\,\min }}\,\matrix{ \nearrow \cr \nearrow \cr } } \right)\,\,\, = {5 \over 3}\,\,{\rm{miles}}$$ $${\rm{hiker}}:\,\,\,{5 \over 3}{\rm{miles}}\,\,\left( {{{60\,\,{\rm{min}}} \over {4\,\,{\rm{miles}}}}\,\matrix{ \nearrow \cr \nearrow \cr } } \right)\,\,\, = 25\,\,{\rm{minutes}}$$ Obs.: arrows indicate licit converters. $$? = 25 - 5\left( * \right) = 20\min$$ $$\left( * \right)\,\,{\rm{used}}\,\,{\rm{while}}\,\,\left( {{\rm{also}}} \right)\,\,{\rm{cyclist}}\,\,{\rm{was}}\,\,{\rm{moving}}!$$ 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 Elite Legendary Member Joined 23 Jun 2013 Posted: 10106 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that a hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. We're asked for the number of MINUTES the cyclist must wait until the hiker catches up. This question requires the use of the Distance Formula - and you might find it easiest to approach the math in small 'steps.' Since the cyclist continues riding for 5 minutes AFTER passing the hiker, we can determine how far the cyclist went during that time. It's worth noting that BOTH the cyclist and the hiker were moving during that time, so the cyclist was moving away from the hiker at a speed of 20 - 4 = 16 miles/hour. Five minutes = 5/60 = 1/12 of an hour. Distance = (Rate)(Time) Distance = (16 miles/hour)(1/12 hour) D = 16/12 = 4/3 of a mile The cyclist stops and waits for the hiker to 'catch up.' Now that we know that distance that the hiker must travel, we can determine how long that would take. Distance = (Rate)(Time) 4/3 miles = (4 miles/hour)(T hour) (4/3)/4 = T 4/12 hour = T 1/3 hour = T Since there are 60 minutes in 1 hour, 1/3 of an hour = 20 minutes Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15192 messages Followed by: 1860 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: GMAT Prep A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up? A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 The OA is C. Rate and time have a RECIPROCAL RELATIONSHIP. The RATE RATIO for the hiker and cyclist = 4 mph : 20 mph = 1:5. Thus: The TIME RATIO for the hiker and cyclist = the reciprocal of the rate ratio = 5:1. Implication: The hiker will take 5 TIMES AS LONG as the cyclist to travel the same distance. Since the cyclist travels for 5 minutes, the hiker will take 5 times as long -- 25 minutes -- to travel the same distance. Thus, the cyclist will have to wait 20 minutes for the hiker to catch up. The correct answer is C. _________________ 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2215 messages Followed by: 17 members Upvotes: 43 BTGmoderatorLU wrote: Source: GMAT Prep A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. the cyclist stops & waits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up? A. 6 2/3 B. 15 C. 20 D. 25 E. 26 2/3 We are given that a cyclist travels at a rate of 20 mph, passes a hiker, and then stops to wait for the hiker after traveling for 5 minutes. Since 5 minutes = 1/12 hours, the cyclist travels a distance of 20/12 = 5/3 miles. During these 5 minutes, the hiker walks 4/12 = 1/3 miles. So the difference between the cyclist and the hiker is 5/3 - 1/3 = 4/3 miles when the cyclist stops and waits for the hiker. Therefore, it will take the hiker (4/3)/4 = 1/3 hour = 20 minutes to catch up with the cyclist. Alternate Solution: Notice that the cyclist travels precisely 5 times as fast as the hiker. Therefore, the distance traveled by the cyclist in 5 minutes will be traveled by the hiker in 25 minutes. Since the hiker had already been walking for 5 minutes when the cyclist stopped to wait for her, the hiker must walk 25 - 5 = 20 more minutes to catch up with the cyclist. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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