Nov 29, 1996
RAY: Back in the old days when my brother used to work, my brother used to have his wife drive him to the train station and then he'd take the train and go to work. Then an hour later, he'd get on the train to come home.
TOM: After lunch.
RAY: Right after lunch. And he'd get to the train station and his wife would meet him there and they'd drive home. Well one day, he decides to leave work early at 11 am. Needless to say, he gets to the train station an hour early. Rather than call his wife, it's a nice day and he decides to hoof it. So he starts walking in the direction she'll be driving. And low and behold, he sees his wife coming up the road and she sees him by the side of the road. They get in the car and they drive home and arrive 20 minutes earlier. Don't forget - she left home at the usual time.
TOM: Of course, she didn't know he was going to leave work an hour early.
RAY: They get home 20 minutes earlier than they would have gotten home. How long was he walking before they met? Notice, there's no mention of how long she was driving, how fast he walked, what train he took, and what any of the distances were. How long was he walking before she picked him up?
TOM: I got it. He was walking for 40 minutes.
RAY: So close.
RAY: Fifty. Because if they arrived home 20 minutes earlier than usual, he saved, by walking, 10 minutes of her travel time to the station and 10 minutes of her travel time from the station. Therefore, he was walking for 50 minutes when she picked him up. You have to put all of the pieces together. He left an hour earlier but she left at the same time and saves 20 minutes of the total trip. It's as if he moved the station 10 minutes closer.
TOM: How did you get 50 minutes out of that?
RAY: Ten minutes...
TOM: Oh 10 and 50 is an hour!
RAY: And 10 and 10 is what?