A freight train 1 mile long goes through a tunnel 2 miles long. The train is traveling 15 mph. How long does it take to pass entirely through the tunnel?
Generalize your answer, that is, find a formula that gives the time for a train miles long to pass through a tunnel miles long traveling at miles per hour.
Solution
The engine of the train travels the two miles of the tunnel in of an hour. At the moment the engine begins to emerge, the end of the train is halfway through. It goes the extra mile in of an hour. The whole train is out of the tunnel in of an hour, or minutes.
The same reasoning works in general. For the engine to begin to emerge from the tunnel takes hours: miles at mph. For the end of the train to emerge takes another hours: miles at mph. The total time required: .