# Riding Against the Wind Puzzle - Solution

### The Puzzle:

A bicycle rider went a mile in three minutes with the wind, and returned in four minutes against the wind. How fast could he ride a mile if there was no wind?

### Our Solution:

Contrary to the popular answer to problems of this kind, that if a rider goes a mile in three minutes with the wind, and returns against the wind in four minutes, that 3 and 4 equal 7, should give a correct average, so that his time should be taken to be 3 and a half minutes. We find this answer to be incorrect, because the wind has helped him for only three minutes, while it has worked adversely for four minutes.

If he could ride a mile in three minutes with the wind, it is clear that he could go a mile and a third in four minutes, and one mile in four minutes against the wind.

Therefore two and one-third miles in eight minutes gives his actual speed, because the wind helped him just as much as it has retarded him, so his actual speed for a single mile without any wind would be 3 minutes and 25 and 5/7 seconds.

If he could ride a mile in three minutes with the wind, it is clear that he could go a mile and a third in four minutes, and one mile in four minutes against the wind.

Therefore two and one-third miles in eight minutes gives his actual speed, because the wind helped him just as much as it has retarded him, so his actual speed for a single mile without any wind would be 3 minutes and 25 and 5/7 seconds.

Puzzle Author: Loyd, Sam

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