Walk the Dog.

Apr 09, 2007

RAY: I've received this puzzler over the years from a whole bunch of different people. And I got this most recent one from the same guy who sent in the cow and kine puzzler. It made me decide to use it. I figure if he's going to be in trouble, I might as well get him in more trouble. Here it is - I had to post-obfuscate, but it's basically the same.

A man who owned a dog lived at the bottom of the hill. It was their habit every morning to walk the three kilometers to the top of the hill and then back for exercise, for both the dog and the owner. Well, time has gone on and the dog has gotten older. The man still walks to the top of the hill every morning, but the elderly dog can't quite keep up with him.

So now what they do is this: The man starts out at his usual steady pace and the dog follows but at half the man's speed. So when the man reaches the top he turns around and starts back down, maintaining the same steady pace. Before long he meets the dog coming up the hill and at this point the dog turns around and starts back down again.

And I'll add an additional wrinkle, because they're going down the hill, now the man and the dog walk at the same speed down the hill because gravity's helping the dog down the hill. And they get home together.

Two part question: What kind of a dog is it? And two, how far does the dog walk?
RAY: Here's the answer. When the man has reached the top of the hill, he's walked three kilometers because the whole trip is six. But the dog has walked only a kilometer and a half.

TOM: Correct.

RAY: Now the man at that point starts walking back down the hill. But the dog doesn't know that and continues to walk up the hill.

TOM: Right.

RAY: At some point they're going to meet, and the question is, where do they meet? Because the owner walks twice as fast as the dog and they start 1.5 kilometers apart, right?

TOM: Right.

RAY: The man will have walked one kilometer down the hill, while the dog is walking up the hill and goes a half a kilometer. So the dog will have walked a kilometer and a half, plus a half a kilometer. They'll meet at the two kilometer mark, two kilometers from the house.

TOM: Uh-huh.

RAY: So when the dog turns around and heads for home he will have walked two kilometers up the hill and two kilometers down the hill.

TOM: Excellent.

RAY: Do we have a winner?

TOM: The winner this week is Linda Soyarz from Aiken, South Carolina, and for having her answer selected at random from among both of the correct answers that we got, I mean the hundreds of correct answers...

RAY: Thousands.

TOM: Linda is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com, where she can get a copy of our CD of great stories that we have told on the air called, "Once Upon a Car Fire." Congratulations Linda.

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