Two Trains and a Bee

Nov 27, 1999

RAY: Ha! We're back. You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to discuss cars, car repair and, uh, the new Puzzler.

TOM: Which you said is locomotive in nature.

RAY: Well, it is, I suppose. Here it is.

TOM: Yeah.

RAY: You have two trains on the same track.

TOM: Ah! It is locomotive in nature!

RAY: Speeding toward one another.

TOM: I had this problem in the eighth grade.

RAY: You did? Did you get it?

TOM: One of them's going a hundred miles an hour.

RAY: No, no, no, no. I'm going to make it even simpler.

TOM: Yeah.

RAY: I'm going to make it simpler, and I'm going to work the numbers, you know?

TOM: OK.

RAY: So you can do it in your head.

TOM: Will this require drawing a little picture?

RAY: I want to see all work.

TOM: All the work. OK.

RAY: So, if you're going to send an answer in, I want to see the work.

TOM: You want to see the work? OK. So...

RAY: The trains are 150 miles apart.

TOM: One hundred fifty. OK.

RAY: On the same track, but going clearly in opposite directions.

TOM: They're always on the same track, aren't they? You'd think they'd know by now not to put two trains going in opposite directions on the same track.

RAY: So, they're heading toward each other, all right?

TOM: Yeah. I got it.

RAY: All right. When they are 150 miles apart, a very fast bee flies from the...

TOM: Ha, ha, ha, ha, ha!

RAY: Now, pay attention, damn it!

TOM: Yeah. OK. I got it.

RAY: Flies from the bumper of one train--the front bumper, that is.

TOM: Yeah.

RAY: If trains even have bumpers.

TOM: Yeah.

RAY: To the front bumper of the oncoming train, the other train. And, of course, as soon as it gets there, without losing any time, it turns right around and heads back.

TOM: Yeah.

RAY: So, as these trains are speeding toward each other--chucka, chucka, chucka, chucka, chucka, chucka, bzzzz, chucka, chucka, chucka, bzzzz, chucka, chucka, chucka, chucka, bzzzz, chucka, chucka, chucka, chucka, bzzzz, chucka, chucka, chucka, chucka, bzzzz, bzzzz, bzzzz...you got it?

TOM: All right! I got it! I love it! I was actually getting bzzzzz!

RAY: The bee...the bee flies at 137 1/2 miles per hour.

TOM: Hunh? Really?

RAY: How far will the bee have traveled before he is squashed like a grape?

TOM: Or worse.

RAY: Between 150 tons of mangled steel.

TOM: Yeah, yeah.

RAY: That's the question. You get it?

TOM: Well, how fast are the trains going?

RAY: I told you, didn't I?

TOM: No.

RAY: Didn't I? I left that out?

TOM: You left that out.

RAY: I'm sorry.

TOM: You moron.

RAY: The trains are traveling at 75 miles an hour.

TOM: Are they?

RAY: So, you got two trains, each traveling at 75.

TOM: That's...that's better.

RAY: Seventy-five and 75. They start at 150 miles apart.

TOM: Yeah.

RAY: Notice how that's convenient?

TOM: That's very convenient.

RAY: Right. And the bee...

TOM: Yeah.

RAY: Is flying at 137 1/2 ...

TOM: Oh, you had to make it that hard?

RAY: Miles an hour. So, the question is: How far does the bee fly?

TOM: He flies from the bumper of the first one -

RAY: Back and forth, back and forth.

TOM: Now, when you said the trains are 150 miles apart, we're going to assume that the front of the trains...

RAY: Yes, of course.

TOM: Because if they're...

RAY: The business end of the train.

TOM: The business end of the train. The rest of the train is more than 150 miles.

RAY: As far as the bee is concerned, it's only the front of the train that counts.

TOM: That matters. OK.

RAY: OK.

TOM: So, he's flying from the front of Train A to the front of Train B.

RAY: And then back to A, back to B, back to A, back to, like ping, pong, ping, pong, ping.

TOM: And does he start at the precise moment that they both start?

RAY: Zip, zip, zip, zip.

TOM: Someone says, "Go!" at which point both trains start going, and they immediately go 75 miles an hour. They go from zero to 75 in zero time.

RAY: Well, they...no. They could already have been moving at 75 miles an hour.

TOM: Let's do that. I like that.

RAY: And the bee happens to start his journey the instant they're 150 miles apart.

TOM: I've got it. I got it.

RAY: So the trains have already achieved terminal--and I mean terminal--velocity.

TOM: Yeah. Yeah.

RAY: So, at the instant they crash, how far will the bee, who's flying at 137 1/2 miles per hour, have flown?

TOM: Yeah. This is a great problem.

Answer: 

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 137.5 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.

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