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

by : $33$

 * A Rowing Puzzle
 * A crew can row a certain course upstream in $8 \tfrac 4 7$ minutes,
 * and, if there were no stream, they could row it in $7$ minutes less than it takes them to drift down the stream.


 * How long would it take to row down with the stream?

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: