Henry Ernest Dudeney/Modern Puzzles/33 - A Rowing Puzzle/Solution

by : $33$

 * A Rowing Puzzle

Solution

 * $3 \tfrac 9 {17}$ minutes.

Proof
Let the course be $d$ miles long.

Let $v$ miles per minute be the speed the crew would be able to row in still water.

Let $v_s$ miles per minute be the speed of the stream.

Let $v_u$ miles per minute be the speed upstream.

Let $v_d$ miles per minute be the speed downstream.

Let $t$ minutes be the time taken to row $d$ miles in still water.

Let $t_u$ minutes be the time taken to row $d$ miles upstream.

Let $t_d$ minutes be the time taken to row $d$ miles downstream.

Let $t_s$ minutes be the time taken to drift $d$ miles downstream without rowing.

We have:

Thus:

Multiplying the two results above:

Substituting $t = t_s + 7$:

We reject $t_s = -12$ as $t_s > 0$.

Thus $t_s = 5$ and $t = 12$.

Therefore:

Hence the result.