Two Trains and a Bee

Jul 27, 2020

RAY: This puzzler is locomotive in nature.

You have two trains on the same track, speeding toward one another. The trains are 150 miles apart.

They’re on the same track, heading towards each other. 

When they are 150 miles apart, a very fast bee flies from the bumper of one train--the front bumper, that is--to the front bumper of the oncoming train, the other train (assuming trains have bumpers.)

And, of course, as soon as it gets there, without losing any time, it turns right around and heads back.

So, as these trains are speeding toward each other the bee flies at 137 1/2 miles per hour.

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

By the way, the trains are traveling at 75 miles an hour.



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 train number two.

And then you can say, "Well, in that time, train number one has..." but there’s an easier way.

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?

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