Henry Ernest Dudeney/Modern Puzzles/41 - The Damaged Engine/Solution

by : $41$

 * The Damaged Engine

Solution

 * $200$ miles, of which the first $50$ miles were at $50$ miles per hour, and the rest at $30$ miles per hour.

Proof
Let $d$ miles be the distance from Anglechester to Clinkerton.

Let $v$ miles per hour be the speed of the train when working properly.

Let $d_1$ miles be the distance from Anglechester to where the train malfunctioned.

Let $t$ be the time the train would normally take to travel the journey.

We have: