math 101)

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this is a tricky question pf Math , please type it with more more details and formals 

Deadline : 5 hours 

Question : Pat works in the city and lives in the suburbs.  Every afternoon, Pat gets on a train which arrives at the suburban station at exactly 5pm.  His wife leaves the house before 5pm and drives at a constant speed so as to arrive at the train station at exactly 5pm to pick up Pat.  The route that Pat’s wife drives never changes.

One day, this routine is interrupted, because there is a power failure at work. Pat gets to leave early, and catches a train which arrives at the suburban station at 4pm.  Instead of phoning his wife to ask for an earlier pickup, Pat decides to get a little exercise, and begins  walking home along the route that his wife drives , knowing that eventually  his wife will intercept him, make a uturn, and they will head home together in the car.  This is indeed what happens, and Pat ends up arriving at home 10 minutes earlier than a normal day.  Assuming that Pat’s walking speed is constant, for how many minutes did Pat walk?

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