Henry Ernest Dudeney/Modern Puzzles/43 - The Two Ships/Solution

by : $43$

 * The Two Ships

Solution
The error lies in assuming that the average speeds are equal.

They are not.

The first ship does a mile in $\tfrac 1 {12}$ of an hour outwards and $\tfrac 1 8$ of an hour homewards.

Half of the sum of these fractions is $\tfrac 5 {48}$.

Therefore the ship's average speed for the $400$ miles is a mile in $\tfrac 5 {48}$ of an hour.

The average speed of the second ship is a mile in $\tfrac 1 {10}$ of an hour.