Take a hike
Johnny and Billy’s mom agrees to them attend the Saturday matinee. Before they go into the theater, their mom asks them to go in find out what time the movie is over so she knows what time to return to pick them up. Johnny comes back and tells her the movie ends at 3:00. Mom says she’ll be back at that time to pick them up and drives back home.
It turns out the movie actually ends at 2:30. Rather than wait for half an hour for their mom to arrive, Johnny tells Billy they should start walking home on same path that their mom would take to pick them up. His plan works out because they meet mom along the way and arrive home 10 minutes earlier than they would have had they stayed and waited for mom to arrive at 3:00.
How long did the boys walk before they met their mom?
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1 solution
If the boys and their mother arrive home ten minutes earlier than they would have had they not walked, then the mother drove the car for ten minutes less than she would have. This means that the distance the boys walked, the mother would have driven in five minutes (five minutes to the theatre, five minutes back.) Thus the boys met their mother five minutes before she would have reached the theatre, i.e. at 2 : 5 5 , and therefore they walked for 2 5 minutes.