This was on a programme called "Mind Games" recently.

An engineer was walking through a railway tunnel. When he was a quarter of the way through the tunnel he heard a train approaching from some way behind him.

The train was travelling at such a speed that if the engineer were to run back the way he came in he would just make it out off the tunnel before the train entered. If he ran the other way he would also just make it out of the far end of the tunnel before the train caught him.
Question

If the engineer, at full sprint, was running at 12 miles per hour, how fast was the train going?