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# The early Commuter

## Question

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 along the way.  He gets in the car and drives home.  He arrives home, ten minutes ahead of schedule.  If his wife and train trip always go at the same speed.  How long did the man walk this day?

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55 minutes.

Explanation:

Let's say his wife takes X minutes to drive from home to the train station. It also takes her X minutes to drive back. So, every day (including that one day) she leaves home X minutes before 5 o'clock to meet her husband and they arrive home X minutes after 5. That day they arrived home X-10 minutes after five, so the wife drove 5 minutes less in each direction. She drove X-5 minutes until she met with her husband, which puts the time of their meeting at 4:55 pm. He started walking at 4 pm, so he walked for 55 minutes.

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