Henry Ernest Dudeney/Modern Puzzles/39 - The Two Trains

by : $39$

 * The Two Trains
 * Two railway trains, one $400$ feet long and the other $200$ feet long, ran on parallel rails.
 * It was found that when they went in opposite directions they passed each other in $5$ seconds,
 * but when they ran in the same direction the faster train would pass the other in $15$ seconds.


 * Now, a curious passenger worked out from these facts the rate per hour at which each train ran.
 * Can the reader discover the correct answer?


 * Of course, each train ran with a uniform velocity.

Solution
The faster train went at $54 \tfrac 6 {11}$ miles per hour.

The slower train went at $27 \tfrac 3 {11}$ miles per hour.

Proof
Let $v_1$ feet per second denote the speed of the faster train.

Let $v_2$ feet per second denote the speed of the slower train.

We have:

The result follows on converting $80$ feet per second and $40$ feet per second into miles per hour.