RAY: Last month Tommy and I decided that we were going to take a trip up north to see the foliage. And our wives decided they couldn't stand the thought of being in the car with us, so we were on our own. So we get in the car and Tommy drives the first 40 miles. I drive the rest of the way. We arrive at our destination, we get out of the car, glance at the foliage, and Tommy says, "okay, let's get a cappuccino, let's get out of here." So we turn around and head home on the same road that we used to get there, okay? Tommy drives the first leg of the trip, and I drive the last 50 miles home.
Anyway, when I get home my wife says, "How was the trip?" And I say, "I was with my brother, how good could it have been?" And she says, "Well, who did the driving?" And I explain exactly what I just said. "On the way there Tommy drove the first 40 miles and I drove the rest. On the way back Tommy drove the first leg of the trip and I drove the last 50 miles."
She said, "Yeah, but who did most of the driving?"
I said, "Well, you can figure it out, in fact you can even figure out how much more of the driving was done by that person." Now, I didn't say how long we were gone, how far we went, whose car we tookay, who bought the gas or any of those things. So the question was who drove the most miles and how many more did that person drive?
TOM: Whew.
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 ]
