TOM: Throw your hat in the ring or in the river.
RAY: Oh, here it is. It's the first day of spring or summer or whatever and you decide to rent a little boat at the dock and go for a little boat ride. You're rowing upstream...okay, you with me?
TOM: Upstream.
RAY: Okay, that means there's a current.
TOM: There's a current.
RAY: And you get a mile from the dock, and your hat flies off and lands in the water. It's just a Car Talk hat, so you say, forget it, and you keep rowing. Then ten minutes later you realize that your two tickets to that night's Sleepy La Beef concert are tucked inside the sweatband. So, you turn around, and you start rowing downstream. You're now chasing the hat. And of course you're rowing with the same number of strokes and the same intensity that you were rowing with upstream, and you catch up with the hat right at the dock. The question is: how fast is the current? So, let me go over the salient points here.
TOM: Wow, yeah.
RAY: You go upstream for a mile.
TOM: A mile.
RAY: Against the current.
TOM: The current is working against you.
RAY: The hat falls off into the water. You say, forget it. You keep rowing for ten minutes. At which point, you remember the tickets.
TOM: You turn around.
RAY: You turn around, during which time, that hat is --
TOM: All this time, the hat's been going the other way.
RAY: Going the other way, baby.
TOM: Because the current is pushing it.
RAY: And you catch up with the hat right at the dock where you in fact rented the boat. So, the hat has actually traveled a mile.
TOM: Traveled one mile.
RAY: That's the only thing you really know.
TOM: Yeah, because you dropped it when you were a mile away from the dock, and you caught it at the dock. So the hat, I got that, the hat has traveled; that's a key point.
RAY: That's key, well, and good thing we gave you that information. So, the hat traveled a mile. So, we want to find out how fast the river's going. If we only knew how long the hat was traveling that mile, we could use the famous formula, distance = rate x time --
TOM: And we do know.
RAY: And we do know.
TOM: We do know.
RAY: Because imagine that there is no current, and your hat falls off into the water. If you rode away from the hat for ten minutes, how long would it take you to get back to the hat? It would take you ten minutes.
TOM: Exactly.
RAY: Well, it turns out the current doesn't make any difference, because the same current that's pushing the hat downstream, once you've turned around, is pushing you downstream at the same rate. So, in fact, if you row away from the hat for ten minutes and then turn around when you've decided to go back and retrieve it, it takes you ten minutes to get back to the hat.
TOM: What was the question?
RAY: What row were those Sleepy La Beef tickets in?
TOM: The question was, how fast is the river flowing?
RAY: Right. You row away from the hat for ten minutes. It takes you ten minutes to get back to the hat. So, in fact, you've been rowing for 20 minutes, and the hat, been drifting for 20 minutes downstream, during which time it's gone a mile. So, in a third of an hour, it went a mile. The current must be going at three miles per hour.
TOM: Yeah, and that's all you really had to know, because you know that the hat has gone one mile in 20 minutes. You know that. That's it.
RAY: There you go.
TOM: And that's how fast, the answer is, the river is flowing at one mile in 20 minutes. No one says it's got to be in miles per hour. You didn't tell us that.
RAY: Okay, do we have a winner?
TOM: I don't know. Yes, we have a winner. It's Eugenia, ooh, that was my grandmother's name, you know --
RAY: You're not going to believe this, but I think it was my grandmother's name, too.
TOM: No! What are the chances of that?
RAY: Pretty slim.
TOM: The winner is Eugenia Tillinghast from Lubbock, Texas. And for having her correct answer selected at random from all the correct answers that we got this week, Eugenia is going to get a $25 gift certificate to the Shameless Commerce Division at the Car Talk section of Cars.com, with which she can get our brand spanking new, Evolution of the Modern Mechanic T-shirt. This is a beautiful thing. You may remember that some months ago we held a T-shirt contest, and this is the winning design, and it shows the evolution of the modern mechanic from modern man to neanderthal to cro-magnon and finally, of course, to Click and Clack, the Tappet Brothers. In other words, it goes from homo erectus to homo incorrectus. That's us.
RAY: Well, it's interesting that you should have mentioned this T-shirt, because the fellow who won the T-shirt contest is named Malcolm --
TOM: Malcolm Ross McDonald.
RAY: And it was he who sent in this puzzler that I'm going to be using in the third half of the show today.
TOM: Now, what are the chances of that?
RAY: I just made it up, but it sounded pretty good. So anyway, stay tuned for that. In the meantime, if you have a question about your car or anything else, we'll be happy to give you the wrong answer. The number's 888-CARTALK, that's 888-227-8255. Hello, you're on Car Talk.
[ Car Talk Puzzler ]
