P <----------------------------------------> Q
Total distance =37.5
Total time taken = 2.7 hrs (approx)
Distance between P and Q = 37.5/2 =18.75 km

Total time = time to walk + time to cycle
Avg Speed = 37.5 km/2.7 hours
Speed while walking = W
Speed while cycling = C
Now, had he cycled, he would have spent 40 minutes lesser on the road i.e he would have taken just 2 hours.

So new Avg speed = 37.5 km/2 hours = 18.75 kmph

So? Avg speed is also = (C+W)/2 right ?

i.e. (37.5/2.7) = (C+W)/2 ....(equation 1)
and (37.5)/2 = (C+C)/2 => 2C = 37.5 or C = 37.5/2 or 18.75 kmph

Using value of C in equation 1 => 37.5/2.7 = {(37.5/2)+W}/2
=> 37.5/2.7 = (37.5 +2W)/4 and so on till you get the answer. Now you can definitely find a smarter and shorter way to do this, but atleast now you can easily understand the problem.

singhsubir wrote:A man walks from P to Q and cycles from Q to P, a distance of 37.5 km in all, spending a total of 2 hr 40 min. He would have taken 2/3 hr less had he chosen to cycle the entire distance. What would have been the time taken by him if he had chosen to walk both the ways?

Hi!

We can set up a couple of simple equations to solve this relatively painlessly.

Let's call his one way walking time "W" and his one way cycling time "C". We want to know the time for walking both ways, so we're solving for 2W.

We know that:

W+C = 2h40min

and

W+C = C+C+40

(since it takes 40 minutes more to walk and cycle than to double cycle).

Solving the second equation for C:

W = C + 40
W - 40 = C

And now substituting into the first equation:

W + (W-40) = 2h40min
W + W = 2h40min + 40
2W = 3H20min

Done!

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This is also a great question for common sense and logic - very underused tools on the quant side of the GMAT.

Thinking it through: if double cycling would be 40 minutes less than cycling plus walking, then cycling one-way must take 40 minutes less than walking one way. So, if we're walking 2 ways instead of just one, then we'll add 40 minutes to our time. 2h40min + 40min = 3h20min.

Note that the logic in the above paragraph is identical to the equations we solved above - but if you understand the situation, you don't actually need to do all that math.

* * *

(For future reference, please always include the source and the answer choices, since a lot of strategies involve using the answers.)