Gustav ran 32 meters uphill at a constant speed...

[AAPL]

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!

[DavidG@VeritasPrep]

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

[Scott@TargetTestPrep]

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

Answer: D