Car Trip Trigonometry
RAY: Here's the answer. 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: You could make the distance anything you want, but let's make it 50 miles. So Tom drove the first 40 miles. And I drove the last ten.
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, you will always drive 20 miles more.
RAY: Who's our winner, man?
TOM: The winner is Clark Newhall, from Sandy, Utah. Congratulations Clark!
[ Car Talk Puzzler ]