A commuter is in the habit of arriving at his suburban station each evening exactly at 5 P.M. His wife always meets him there with the car and drives him home. One day he takes an earlier train and arrives at the station at 4 P.M. The weather is pleasant, so instead of telephoning home, he starts walking along the route always taken by his wife. They meet somewhere on the way. He gets into the car, and they drive home, arriving at their house 10 minutes earlier than usual. Assuming that his wife always drives at a constant speed and never varies her route, can you determine how long a time he walked before he was picked up?
The commuter has walked for 55 minutes before his wife picks him up. Because they arrive home 10 minutes earlier than usual, this means that his wife has chopped 10 minutes from her usual travel time to and from the station, or five minutes from her travel time to the station. It follows that she met her husband five minutes before his usual pickup time of 5 P.M., or at 4:55. He started walking at 4 P.M.; therefore, he walked for 55 minutes. The commuter’s speed of walking, his wife’s speed of driving and the distance between home and station are not needed for solving the problem. If you tried to solve it by juggling figures for these variables, you probably found the problem aggravating.
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A version of this puzzle originally appeared in the February 1957 issue of Scientific American.