### Brain Teasers

# Tunnel Vision

A train passes through a long tunnel in the mountains. The train is 125 meters long, and travels at 40 kilometers per hour.

Just as the last car is completely inside the tunnel, a man begins walking from the end of the train to the front. He walks at 5 kilometers per hour and reaches the front of the train just as it emerges into the daylight.

How long is the tunnel?

Just as the last car is completely inside the tunnel, a man begins walking from the end of the train to the front. He walks at 5 kilometers per hour and reaches the front of the train just as it emerges into the daylight.

How long is the tunnel?

### Answer

Let x = the length of the tunnel in meters. The man travels x meters at 45 kilometers per hour (the combined speed of the train and his walking) in the same time that the train travels (x-125) meters at 40 kilometers per hour.The equation x/45 = (x-125)/40 solves to x=1125. Therefore, the length of the tunnel is 1125 meters.

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