8. The Early Commuter

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A COMMUTER IS in the habit of arriving at his suburban station each evening
exactly at five o’clock. His wife always meets the train and drives him home.
One day he takes an earlier train, arriving at the station at four. 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 ten minutes earlier than usual.
Assuming that the wife always drives at a constant speed, and that on this
occasion she left just in time to meet the five o’clock train, can you determine
how long the husband walked before he was picked up?

The answer

The commuter has walked for 55 minutes before his wife picks him up. Since
they arrive home 10 minutes earlier than usual, this means that the 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 pick-up time of five o’clock, or at 4:55. He started
walking at four, therefore he walked for 55 minutes. The man’s speed of
walking, the 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 exasperating.
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