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!
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!
