Sunday, August 29, 2010

Speed of train going through a tunnel

There is a tunnel with a train track and two people are at 1/4th distance from one end of the tunnel. They heard the train sound, and both started running in the opposite directions immediately. Both barely missed the train from hitting. Both run at the same speed. What is the speed of the train?

It is not possible to find the speed of the train with just this information. But, if this kind of question is asked in the interviews, it means, we need to find the speed of the train relative to others like the speed of the person, or the distance of the tunnel etc.

In the above diagram, AB is the tunnel, and AC is 1/4th of the tunnel and BC is 3/4th of the tunnel. The train is at D when they heard the train sound.

The train enters the tunnel at point A. If the train enters the tunnel at point B, then both will not miss the train barely. If the train enters the tunnel at point B, By the time the person travels from C to B, the other person can comfortably cross the tunnel. So, the train enters the at point A only.

Since both barely missed the train, it means, both the train and the first person reached point A at the same time. At that time, the second person would be at the middle of the tunnel. The second person also misses the train barely at point B. It means, by the time, the second person reaches from the middle of the tunnel to B, the train reached from point A to B. It means, the train travels twice faster than the person.

By the time, the first person reached from C to A, the train reached from D to A. From the relative speeds of the person and the train, we can conclude that, DA is double to CA, and half of AB.