RAY: Hi! We're back. You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to talk about cars, car repair and, uh, the answer to last week's locomotive...
TOM: Oh, now I remember it.
RAY: Or, you could say automotive Puzzler.
TOM: Locomotive. I remember it now.
RAY: And I said a trained bee, and I meant a "trained" bee--a bee that had been hit by a train. Anyway, here it is.
TOM: Yeah.
RAY: You have two trains on the same track, speeding toward one another.
TOM: Am I going to need a pencil?
RAY: Get a pencil, yeah.
TOM: Get the pencil.
RAY: Just make a little picture.
TOM: Two trains. There we are.
RAY: The trains are 150 miles apart.
TOM: Mmm-hmm.
RAY: And they're both traveling at 75 mph.
TOM: Seventy-five. And they're on the same track? Did you say that yet?
RAY: Two trains on the same track!
TOM: I'm with you now. Go ahead.
RAY: A very fast bee.
TOM: Yeah.
RAY: Maybe even a trained bee, flies from the front bumper of one train to the front bumper of the other train. And as soon as it gets to the second train, without losing any time in reversing its decision, it turns around, reversing its direction...rather, it turns around and heads back to the first train. And it continues to do this flying back and forth and back and forth, back and forth and forth and back, and back and forth.
TOM: Yeah.
RAY: OK, you got that now?
TOM: I got it.
RAY: So, as the train is...
TOM: So, each time it goes, it goes a shorter distance, of course.
RAY: Of course.
TOM: Because the trains are hurtling toward each other at 75 miles an hour.
RAY: Exactly. Exactly.
TOM: Yeah.
RAY: Exactly. OK?
TOM: Whoof! So, they go voom! Voom! Voom! Voom! Voom!
RAY: So, you got all these little pieces you're going to have to add up.
TOM: Those are going to have to add up.
RAY: Diminishing little series, here. You got that?
TOM: Until, WHAP!
RAY: Well, I didn't mention yet that the bee flies at 137.5 miles an hour.
TOM: Excellent.
RAY: And the question is, very simply: How far will the bee have traveled before he's squashed like the bug that he is between the bumpers of the two trains?
TOM: Yeah.
RAY: Now, you could sit down and you could draw the little picture, and you could say, "Well, let me see. If he's flying at 137 miles an hour, and the other train is coming at 75, then that's a combined velocity of 212.5." You can figure out, in fact, how far he travels before he reaches the bumper of the train number two.
TOM: Yeah. Yeah, sure.
RAY: And then you can say, "Well, in that time, train number one has..."
TOM: Train number one has gone, yeah. You could do that.
RAY: You could do that. But, you could also do it the easy way. It isn't the cowboy way...
TOM: But it is the easy way.
RAY: According to our pals Riders in the Sky, but it is the easy way. Now, knowing that the trains are 150 miles apart and traveling at 75 miles an hour, in one hour they will have crashed.
TOM: Really?
RAY: Yeah.
TOM: No kidding!
RAY: So, if the bee is traveling at 137.5 miles an hour, how far will he travel in an hour?
TOM: 137.5 miles.
RAY: And that is...
TOM: And that is the answer.
RAY: The answer.
TOM: And isn't that good?
RAY: Yeah. And that is...that is a...
TOM: How many eighth-grade kids are going to get that in their little test next week?
RAY: They may. They may. Do we have a winner?
TOM: Yeah, of course, we got a winner. Becky Slager from Raleigh, North Carolina. And for having her answer selected at random from among all the...
[ Car Talk Puzzler ]
