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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 ## Alex and Brenda both stand at point X. Alex begins to walk tagged by: BTGmoderatorLU ##### This topic has 4 expert replies and 1 member reply ### Top Member ## Alex and Brenda both stand at point X. Alex begins to walk ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Manhattan Prep Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex? A. R-4 B. R/(R+4) C. R/(R-8) D. 8/(R-8) E. 2R - 4 The OA is C. ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 829 messages Followed by: 4 members Let T the time that Alex will have been walking when Brenda has covered twice as much distance as Alex. In T hour Alex will cover 4T miles; Since Brenda begins her journey 1 hour later than Alex then total time for her will be T - 1 hour, and the distance covered in that time will be R(T-1); We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T = R(T-1) --> 8T=RT-R --> T=R/(R-8). Hence, C is the correct answer. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1434 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Manhattan Prep Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex? A. R-4 B. R/(R+4) C. R/(R-8) D. 8/(R-8) E. 2R - 4 Let´s explore a particular case, say R=9. In this case we have: FOCUS: T (as a function of R=9) Alex: 4T miles travelled after T h. Brenda: 9(T-1) miles travelled after (T-1) h. From the question stem, we know that: 9(T-1) = 2*4T to find T = 9 (h). In short: when R=9, the "target" is also (by coincidence) 9. (A) R-4 = 5 is OUT (B) R/(R+4) = 9/13 is OUT (C) R/(R-8) = 9 is a SURVIVOR (D) 8/(R-8) = 8 is OUT (E) 2R-4 = 14 is OUT There was just one SURVIVOR, therefore this survivor must be the solution to the general case. It´s done. 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 09 Oct 2010 Posted: 1434 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Manhattan Prep Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex? A. R-4 B. R/(R+4) C. R/(R-8) D. 8/(R-8) E. 2R - 4 Let´s REALLY solve the problem, using the WINNING TRIAD and UNITS CONTROL, one of the most powerful tools of our method! DATA: $${\rm{Alex}}\,\,\left( A \right)\,\,:\,\,\,{{4\,\,{\rm{miles}}} \over {1\,\,\,{\rm{h}}}}\,\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,T\,\,\,\,{\rm{h}}$$ $${\rm{Brenda}}\,\,\left( B \right)\,\,:\,\,\,{{R\,\,{\rm{miles}}} \over {1\,\,\,{\rm{h}}}}\,\,\,\,\,\,\,\left( {R > 8} \right)\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\left( {T - 1} \right)\,\,{\rm{h}}$$ FOCUS: $${\rm{?}}\,\,\,{\rm{:}}\,\,\,\,T = f\left( R \right)$$ DATA-FOCUS CONNECTION: $$\underbrace {\left( {T - 1} \right)\,\,{\rm{h}}\,\,\,\left( {{{R\,\,\,{\rm{miles}}} \over {1\,\,\,{\rm{h}}}}\matrix{ \nearrow \cr \nearrow \cr } } \right)}_{{\rm{distance}}\,\,{\rm{travelled}}\,\,{\rm{by}}\,\,B}\,\,\,\,\,\mathop = \limits^{{\rm{question}}\,\,{\rm{stem}}} \,\,\,\,\,2\,\, \cdot \,\,\,\underbrace {T\,\,{\rm{h}}\,\,\,\left( {{{4\,\,\,{\rm{miles}}} \over {1\,\,\,{\rm{h}}}}\matrix{ \nearrow \cr \nearrow \cr } } \right)}_{{\rm{distance}}\,\,{\rm{travelled}}\,\,{\rm{by}}\,\,A}\,\,$$ Obs.: arrows indicate licit converters. $$\left( {T - 1} \right)R = 8T\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\,\,:\,\,\,T\left( {R - 8} \right) = R\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{R\, \ne \,8} \,\,\,\,\,\,\,\,?\,\,\,:\,\,T = {R \over {R - 8}}$$ 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 Apr 2015 Posted: 2244 messages Followed by: 17 members Upvotes: 43 BTGmoderatorLU wrote: Manhattan Prep Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex? A. R-4 B. R/(R+4) C. R/(R-8) D. 8/(R-8) E. 2R - 4 Let t = the number of hours Alex is walking and thus (t - 1) = the number of hours Brenda is biking. We can create the equation: 2(4t) = R(t - 1) 8t = Rt - R R = Rt - 8t R = t(R - 8) R/(R - 8) = t Answer: C _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10109 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that Alex and Brenda both stand at point X, Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour - and ONE HOUR later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. We're asked, if R > 8, then which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered TWICE as much distance as Alex. This question can be solved by in a number of different ways, including by TESTing VALUES. We're told that Alex walks 4 miles per hour and, an hour later, Brenda starts biking at R miles per hour. Let's say that Alex walks for 2 HOURS; that would be 8 total miles. The question asks us to focus on Brenda's travel covering TWICE Alex's distance, so we can build all of our work around the two hours that Alex traveled. Alex = 2 hours, 8 total miles Brenda = 1 hour, 16 total miles Although the prompt doesn't clearly state it, it asks for the total number of hours that Alex traveled at the point that Brenda had traveled twice Alex's distance. Thus, we're looking for an answer that equals 2 when R = 16. Answer A: 12 NOT a match Answer B: 16/20 NOT a match Answer C: 16/8 = 2 This IS a match Answer D: 8/8 = 1 NOT a match Answer E: 16^2 - 4 = NOT a match Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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