Train in Tunnel

A freight train that is 1 mile long goes through a tunnel that is 2 miles long. If the train is traveling at 15 miles per hour, how long does it take it to pass completely through the tunnel?

Part 2: Generalize: the train is n miles long; the tunnel is m miles long, and the train is going r miles per hour. The answer this time will of course be a formula.

Show/Hide Solution

The nose of the train travels the two miles of the tunnel in 2/15 of an hour. As the nose (OK, the engine) reaches the end of the tunnel, the tail of the train (the observation car, or the caboose if they still used them) is exactly halfway through, so it goes the last mile in another 1/15 hour. So the train is completely through the tunnel in 3/15 hours or 12 minutes.

Part 2: The train goes n + m miles, at r mph, so that’s (n + m)/r hours.

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