Car Trip Trigonometry

RAY: Well, you could make it complicated, you could say "Well, gee, I have don't have enough information. I don't know the distance, I don't know the speed, I don't know anything," but I always like to boil these problems down to what I call the limiting case. And I said that you drove the first 40 miles and I drove the rest, okay. And then on the way back you drove the first leg and I drove the last 50.

TOM: Right.

RAY: Well, you could make the distance anything you want, but let's make it 50 miles.

TOM: The whole distance.

RAY: So you drove the first 40.

TOM: Limit theory.

RAY: I drove the last ten.

TOM: Right. Um hm.

RAY: On the way home you didn't drive at all.

TOM: No, you drove the whole 50 miles.

RAY: I drove 50 miles, how many miles did I drive? 60 miles. How many miles did you drive? 40. How many more miles did I drive? 20 miles.

TOM: So no matter what that distance is in between...

RAY: It's always 20 miles.

TOM: You will always drive 20 miles more.

RAY: Who's our winner, man?

TOM: The winner is Clark Newhall, from Sandy, Utah.

[ Car Talk Puzzler ]