Between Two Trains

by | Brain Teasers

This month we have another classic-style brain teaser.  This one requires some math, but as usual, it also requires some clever problem-solving and reasoning!  Enjoy!

Two trains leave two towns that are 100 miles apart. They travel toward each other at rates of 30 mph and 20 mph respectively.

A bumblebee flying at the rate of 75mph starts out just as the faster train departs the train station, and flies to the slower train. The bee then turns around and goes back to meet the faster train. Then it turns around again, etc., and it and keeps flying back and forth between the trains until the trains meet. How far does the tired bumblebee fly?


Answer:

The answer is 150 miles. The easiest way to solve this is to simply figure out how long it will take the trains to meet and then figure out how far the bee will have traveled in that time (since it is traveling at a constant rate of 75mph). Since the trains are traveling at 20 and 30 mph respectively, they will collectively travel 50 miles of the distance between them every hour. So they will cover the 100 miles in 2 hours. Since the bee is traveling at a constant rate of 75 mph it will cover 150 miles in 2 hours.