Henry Ernest Dudeney/Modern Puzzles/32 - Riding in the Wind

by : $32$

 * Riding in the Wind
 * A man on a bicycle rode a mile in $3$ minutes with the wind at his back,
 * but it took him $4$ minutes to return against the wind.


 * How long would it take him to ride a mile if there was no wind?


 * Some will say that the average of $3$ and $4$ is $3 \tfrac 1 2$, and it would take him $3 \tfrac 1 2$ minutes.
 * That answer is entirely wrong.

Solution

 * $3 \tfrac 3 7$ minutes.

Proof
Let $v_w$ miles per minute be the speed of the wind.

Let $v_m$ miles per minute be the speed of the man without the wind.

Let $t$ minutes be the time taken to ride $1$ mile with no wind.

We have: