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Every day, a wife picks up her husband at train station at 5. One day he arrives early at 4 and he begins to walk home along the road which his wife would be traveling. She meets him and takes him the rest of the way. If he would have waited at the train station, she would have arrived there at 5. As it turned out, they reached home 20 minutes early. What time was it when she picked him up?

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It was 4:50

If they made it home 20 minutes early, then the trip was 20 minutes shorter. Then it was 10 minutes shorter going, and 10 minutes shorter coming back home. Since it was 10 minutes shorter going, then she picked him up at 10 'til 5:00, or 4:50.