Nov 16, 2002
RAY: Last month, Tommy and I decided that we were going to take a trip north to see the foliage. Tommy drove the first 40 miles. I drove the rest of the way. We looked at the foliage for three or four minutes, then decided to head home.
We took the same route home.
On the way back, Tommy drove the first leg of the trip and I drove the last 50 miles.
I got home and my wife said, "Who did the driving?"
I explained that Tommy drove the first 40 miles, then I drove the rest of the way. On the way back, Tommy drove the first leg of the trip, and I drove the last 50 miles.
She said, "But who did most of the driving?"
I told her, "You can figure it out. In fact, you can even figure out how much more of the driving was done by that person."
And that's the question. Who drove the most -- and how many more miles did that person drive?
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.
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.