Answer to March 18, 2002 Problem |
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The Train and Bee Problem Two trains, 150 miles part, are approaching each other on the same track, each traveling 75 mph. A bee, perched on the front of train A, begins to fly at a speed of 137.5 mph toward train B; on reaching train B, it reverses direction, always flying at the same speed of 137.5 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:
Because the trains are 150 miles apart and
are approaching each other at a relative velocity
of 150 mph, they will collide at the end of one
hour. According to mathematical folklore, mathematician 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!
John von Neumann would have solved this week's
problem in the following manner:
An interesting twist to this problem would have been asking the same question but have the bee travel at 37.5 mph instead of 137.5 mph! Then it would travel 0 miles since the train would squash it at the beginning since the train is travelling twice as fast as the bee!!
Rich Murray sent in the following correction to the
paragraph above:
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1. Richard K. Johnson | La Jolla, California |
2. Walt Arrison | Philadelphia, Pennsylvania |
3. Rick Jones | Kennett Square, Pennsylvania |
4. Renata Sommerville | Austin, Texas |
5. Keith Mealy | Cincinnati, Ohio |
6. David & Judy Dixon | Bennettsville, South Carolina |
7. Rich Murray | Ridgetown, Ontario, Canada |
8. John Beasley | Winchester, Virginia |
9. Laurence O'Neill | Winchester, Virginia |
10. James Alarie | University of Michigan -- Flint, Michigan |
11. John Funk | Ventura, California |
12. David Powell | Winchester, Virginia |
13. George Gaither | Winchester, Virginia |
14. Tori Eads | Winchester, Virginia |
15. Justin Collins | Winchester, Virginia |