You need to go from point A to point B, and then back to point A. Points A and B are 20 miles apart. You go to point B at a constant speed of 15 miles per hour. If you want your overall speed to be 30 miles per hour, how fast would you have to go from point B back to point A?

(In reply to Puzzle Solution With Explanation by K Sengupta)

By the problem, the length of the journey from A to B is equal to the length of the return journey from B to A.

Consequently, the average speed for the entire trip of A to B and back is equal to the harmonic mean between the speed of the onward journey and the speed of the return journey.

Let the speed during the return journey be r miles per hour.

Then, we must have:

1/15 + 1/r = 2/30
or, 1/r = 1/15 - 1/15 = 0
or, r = 1/0, which is undefined.
This leads to a contradicition.

Consequently, it would be impossible to achieve an overall speed of 30 miles per hour.   
 

Posted by K Sengupta on 2008-03-30 06:24:26