Mr. Smith drove at a steady clip along the highway, his wife beside him. “Have you noticed,” he said, “that those annoying signs for Flatz beer seem to be regularly spaced along the road? I wonder how far apart they are.” Mrs. Smith glanced at her wristwatch, then counted the number of Flatz beer signs they passed in one minute. “What an odd coincidence!” exclaimed Mr. Smith. “When you multiply that number by 10, it exactly equals the speed of our car in miles per hour.” Assuming that the car’s speed is constant, that the signs are equally spaced and that Mrs. Smith’s minute began and ended with the car midway between two signs, how far is it between one sign and the next?
The curious thing about this problem is that it is not necessary 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, we are told, is 10x miles per hour. In 10x miles it will pass 60x signs, so in one mile it will pass 60x / 10x, or 6, signs. The signs, therefore, are 1⁄6 mile, or 880 feet, apart.
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A version of this puzzle originally appeared in the October 1960 issue of Scientific American.