Two missiles speed directly toward each other, one at 9,000 miles per hour and the other at 21,000 miles per hour. They start 1,317 miles apart. Without using pencil and paper, calculate how far apart they are one minute before they collide.
The quickest way to solve this problem is to run the scene backward in time. A minute before the crash, the 9,000-mile-per-hour missile is 150 miles from the meeting point, and the 21,000-mile-per-hour missile is 350 miles from the same point, making the distance between them 500 miles.
Editor’s Note (2/13/25): We have gotten many messages describing an even simpler way to solve this puzzle: From one missile’s frame of reference, the other is traveling at 9,000 + 21,000 = 30,000 miles per hour. Thus, one minute before the crash, the missiles are 30,000 / 60 = 500 miles apart.
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A version of this puzzle originally appeared in the August 1958 issue of Scientific American.