Mr. P drove at a steady clip along the highway, his wife beside him. "Have you noticed," he said, "that those annoying signs for Wild and Wonderful West Virginia seem to be regularly spaced along the road? I wonder how far apart they are." Mrs. P glanced at her watch, then counted the number of signs they passed in one minute. "What an odd coincidence!" exclaimed Mrs. P. "When you multiply that number by ten, it exactly equals the speed of your car in miles per hour." Assuming that the car's speed is constant, that the signs are equally spaced, and that Mrs. P's minute began and ended with the car midway between two signs, how far is it between one sign and the next? |
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Answer: The curious thing about this problem
is that you do not need to know the car's
speed to determine the spacing of the signs.
Let x be the number of signs passed in one minute. In an hour, the car will pass 60x signs. The speed of the car is 10x miles per hour. In 10x miles, it will pass 60x/10x, or 6 signs. The signs therefore are 1/6 mile, or 880 feet, apart. |
| From: Martin Gardner's New Mathematical Diversions published by the M.A.A. in 1995. |
| 1. Nate Zuckerman | Winchester, VA |
| 2. Wes Blackwell | Winchester, VA |
| 3. Michael Leatherman | Winchester, VA |
| 4. Matt Leatherman | Winchester, VA |