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

by : $41$

 * The Damaged Engine
 * We were going by train from Anglechester to Clinkerton, and an hour after starting some accident happened to the engine.


 * We had to continue the journey at $\tfrac 3 5$ of the former speed, and it made us $2$ hours late at Clinkerton,
 * and the driver said that if only the accident had happened $50$ miles farther on the train would have arrived $40$ minutes sooner.


 * Can you tell from that statement just how far it is from Anglechester to Clinkerton?

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: