Two Trains and a Bee

Nov 23, 2013

RAY: You have two trains on the same track speeding toward one another. The trains are 150 miles apart, 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: When they are 150 miles apart, a very fast bee flies from the front bumper of one train to the front bumper of the oncoming train. And, of course, as soon as it gets there, without losing any time, it turns right around and heads back.

TOM: Yeah.

RAY: The bee flies at 137 1/2 miles per hour. How far will the bee have traveled before he is squashed like a grape?

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. So, the question is: How far does the bee fly?


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, 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. 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 the answer.

TOM: And isn't that good? 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. Congratulations, Becky.

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