hardlogic

Walking home one day, you take a short cut along the train tracks. The tracks cross a narrow bridge over a deep gorge. At the point you are 3/8 of the way across the bridge, you hear the train whistle somewhere behind you. You charge across the bridge, and jump off the track as the train is about to run you down. As it happens, if you had gone the other way, you would have reached safety just before being run over as well. If you can run ten miles per hour, how fast is the train moving?

The train is moving at 40 miles per hour. Imagine that a friend is walking with you. When the train whistle blows, you head away from the train, he heads toward it. When he reaches safety, you will be 6/8 (or 3/4)of the way across the bridge, and the train will have just reached the bridge. For the train to cross 4/4 of the bridge in the time you cross the remaining 1/4, the train must be moving four times your speed.

Why this works

This riddle is a clever exercise in relative speed and distance. When you hear the train whistle, you start running away from it, covering the remaining 1/4 of the bridge, while your friend runs toward the train and reaches safety at the end of the bridge. Since you’re 3/8 of the way across, your friend is already 5/8 of the way when he reaches safety, meaning the train has traveled the entire bridge in the time it took you to run that last stretch. The key insight is that for the train to cover 4/4 of the bridge while you only cover 1/4, it must be moving four times your speed, which calculates to 40 miles per hour when you run at 10 miles per hour.

Common Wrong Answers

“20 miles per hour”

This guess is incorrect because it suggests the train is moving at only twice the speed of the person running, which would not allow it to reach the bridge in time to hit the person when he is only 1/4 of the way across.

“30 miles per hour”

This guess also underestimates the speed of the train. At 30 miles per hour, the train would still not be fast enough to reach the edge of the bridge by the time the person runs the remaining distance, given the calculations based on their relative speeds.

“50 miles per hour”

While this guess is faster than the correct answer, it does not fit the scenario described in the riddle. The train's speed must be precisely four times the runner's speed, and 50 miles per hour exceeds that requirement.

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