Answer to October 19, 1998 Problem |
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The Bee Problem Two trains, 100 miles part, are approaching each other on the same track, each traveling 50 mph. A bee, perched on the front of train A, begins to fly at a speed of 75 mph toward train B; on reaching train B, it reverses direction, always flying at the same speed of 75 mph, until it once more reaches train A, whereupon it again reverses direction and flies toward train B, and so on. How far does the bee fly before it and the two trains collide? |
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Solution to Problem:
Because the trains are 100 miles apart and
are approaching each other at a relative velocity
of 100 mph, they will collide at the end of one
hour. Since the bee is travelling at 75 mph for one hour, it must travel 75 miles. According to mathematical folklore, John von Neumann was enjoying himself at a cocktail party, when another guest proposed a similar problem to him. Von Neumann solved the problem instantaneously by summing an infinite series in his head! He used the formula for the sum of an infinite geometric series: Sum = a1 / (1 - r) |
| 1. Trey Genda | Winchester, VA |
| 2. Andrew Crosby | Winchester, VA |
| 3. Michael Leatherman | Norfolk, VA |