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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 ## Gustav ran 32 meters uphill at a constant speed... tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Gustav ran 32 meters uphill at a constant speed... Gustav ran 32 meters uphill at a constant speed, then he ran 36 meters downhill at a faster constant speed so that his downhill speed was faster by 2 meters per second than his uphill speed. Running uphill took Gustav 2 seconds more than running downhill. Gustav's speed running downhill was how many meters per second? A. 2 B. 3 C. 4 D. 6 E. 8 The OA is D. Speed uphill = S Speed downhill = S + 2 Time uphill = T Time downhill = T - 2 Distance / Speed = Time $$\frac{32}{S}-\frac{36}{S+2}=2,\ then,\ \frac{32\left(S+2\right)-36S}{S\left(S+2\right)}=2$$ $$64-4S=2S^2+4S\ =2S^2+8S-64$$ Solving for S, $$2\left(S^2+4S-32\right)=2\left(S-4\right)\left(S+8\right)$$ The Speed can't be negative, then S=4 (speed uphill). Finally, speed downhill will be, 6 meters per second. Is there a strategic approach to this PS question? Can any experts help, please? Thanks! ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 AAPL wrote: Gustav ran 32 meters uphill at a constant speed, then he ran 36 meters downhill at a faster constant speed so that his downhill speed was faster by 2 meters per second than his uphill speed. Running uphill took Gustav 2 seconds more than running downhill. Gustav's speed running downhill was how many meters per second? A. 2 B. 3 C. 4 D. 6 E. 8 The OA is D. Speed uphill = S Speed downhill = S + 2 Time uphill = T Time downhill = T - 2 Distance / Speed = Time $$\frac{32}{S}-\frac{36}{S+2}=2,\ then,\ \frac{32\left(S+2\right)-36S}{S\left(S+2\right)}=2$$ $$64-4S=2S^2+4S\ =2S^2+8S-64$$ Solving for S, $$2\left(S^2+4S-32\right)=2\left(S-4\right)\left(S+8\right)$$ The Speed can't be negative, then S=4 (speed uphill). Finally, speed downhill will be, 6 meters per second. Is there a strategic approach to this PS question? Can any experts help, please? Thanks! You could always back-solve. Say we tested C, 4 meters per second. If he ran downhill for 36 meters at that speed, it would take him 36/4 = 9 seconds. If he ran downhill at 2 meters/sec faster than he ran uphill, he'd have run 32 meters uphill at a speed of 4-2 = 2 meters per second. This would have taken him 32/2 = 16 seconds. The gap: 16 - 9. = 7 seconds. This should be 2 seconds. (Note, at this point, that you'd want to try higher values - if he ran downhill at 2 meters per second, he'd have run uphill at 0 meters per second!) Test D, 6. If we ran downhill for 36 meters at 6 meters/second, it would have taken him 36/6 =6 seconds. If he ran downhill at 6 meters/second, he'd have run uphill at 4 meters per second. He's have covered the 32 meters uphill in 32/4 = 8 seconds. The gap: 8 - 6. = 2. That's what we want! The answer is D _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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AAPL wrote:
Gustav ran 32 meters uphill at a constant speed, then he ran 36 meters downhill at a faster constant speed so that his downhill speed was faster by 2 meters per second than his uphill speed. Running uphill took Gustav 2 seconds more than running downhill. Gustav's speed running downhill was how many meters per second?

A. 2
B. 3
C. 4
D. 6
E. 8

We can let x = the downhill speed, and thus x - 2 = the uphill speed. We can create the equation:

32/(x - 2) = 36/x + 2

32/(x - 2) = (36 + 2x)/x

(x - 2)(36 + 2x) = 32x

36x + 2x^2 - 72 - 4x = 32x

2x^2 - 72 = 0

2x^2 = 72

x^2 = 36

x = 6

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Scott Woodbury-Stewart
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scott@targettestprep.com

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