Problem Solving

A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?

A. 36

B. 38

C. 40

D. 42

E. 44

Ans : C

Need techniques to answer such questions in minimum time

coolhabhi wrote:A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?

A. 36

B. 38

C. 40

D. 42

E. 44

In every case, the distance is THE SAME.
Since d = (rate)(time), we get:
(new rate)(new time) = (actual rate)(actual time).

If he had moved 3 kmph faster, he would have taken 40 minutes -- in other words, 2/3 hour -- less.
Since (new rate)(new time) = (actual rate)(actual time), we get:
(r + 3)(t - 2/3) = rt
rt - (2/3)r + 3t - 2 = rt
-(2/3)r + 3t = 2
-2r + 9t = 6.

If he had moved 2 kmph slower, he would have taken 40 minutes -- in other words, 2/3 hour -- more.
Since (new rate)(new time) = (actual rate)(actual time), we get:
(r - 2)(t + 2/3) = rt
rt + (2/3)r - 2t - (4/3) = rt
(2/3)r - 2t = 4/3
2r - 6t = 4.

Adding together the equations in blue, we get:
(-2r + 9t) + (2r - 6t) = 6+4
3t = 10
t = 10/3.

Substituting t = 10/3 into 2r - 6t = 4, we get:
2r - 6(10/3) = 4
2r - 20 = 4
2r = 24
r = 12.

Thus:
d = rt = (12)(10/3) = 40.

The correct answer is C.

This problem seems a bit too complex for the GMAT.