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.