### Brain Teasers

# The Length of the Train

Al and Ben are standing back to back next to a railroad track. When the front of a train passes them, Al starts to walk in the opposite direction of the train, while Ben starts to walk in the same direction as the train. Each stops walking when the back of the train passes him. If the two of them walk at the same speed, and Al walks exactly 30 feet, and Ben walks exactly 45 feet, how long is the train?

### Answer

The train is 180 feet long.When the back of the train passes Al, he and Ben have both walked 30 feet, meaning Ben will walk 15 feet more when the train passes him. 30 feet that Al walks plus 45 feet that Ben walks makes 75 feet that the back of the train travels in the same time that Ben walks 15 feet, meaning the train is 5 times as fast as Al and Ben.

In the time it takes Al to walk 30 feet, the front of the train moves 150 feet. This distance plus the 30 feet that Al has walked equals 180 feet.

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