# What Speed Was the Train Moving

Rodger was trying to take a short cut through a very narrow tunnel when he heard the whistle of an approaching train behind him.  Having reached three-eighths of the length of the tunnel, he could have turned back and cleared the entrance of the tunnel running at 10 miles per hour just as the train entered. Alternatively, if he kept running forward, the train would reach him the moment he would jump clear of the tracks (at the exit.)

At what speed was the train moving?

### 3 guesses to What Speed Was the Train Moving

• Matt

40 mph

If they are going the same direction, the train arrives at the tunnel when the guy has covered 3/8ths of the 5/8ths he needs to go. Thus, the guy has 1/4 of the distance to go and the train has the entire length. Since they arrive at the same time , the train must be going 4x faster than the guy.

• Crabman

The train travels the length of the tunnel in the same time the person travels (the difference between 5/8 – 3/8 = 2/8 =) 1/4 the length of the tunnel. So the train is traveling 4 times the speed of the person: 40mph

• Matt, you are today’s winner!
At 40 miles per hour. The train would enter the tunnel when John was still two-eighths from the exit or a quarter of the tunnels length. If the train was to reach him at the exit, it would have to travel at four times Rodger’s speed, i.e. 40 miles per hour.