## Tunnel Train

#### Problem

A train, length ½ mile, travelling at a constant speed of 30 miles per hour enters a tunnel which is 2 miles long. How long will it take for the train to completely pass through the tunnel?

#### Solution

If the train is travelling at a speed of 30 miles per hour (60 minutes), this is equivalent to 1 mile in 2 minutes.

It can be seen that the train will need to travel a distance of 2.5 miles to pass completely through the tunnel. If the train travels 1 mile in 2 minutes, it will travel 2.5 miles in 2.52 = 5 minutes .

If the train, travelling at a different constant speed, takes 4 minutes to pass completely through the same tunnel, how fast is it travelling?

Problem ID: 104 (Feb 2003) Difficulty: 2 Star