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?
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.
