The fast watch that is right again in 15 days

Question

An old analog watch runs fast, gaining 2 minutes every hour. Right now you set it to the correct time. How long until the watch again displays the exact correct time (by coincidence)?

Accepted Answer

The watch shows the correct time again after 15 days. When does a fast clock "look right" again? An analog watch face repeats every 12 hours. So the watch reads correctly whenever it has run ahead by a whole multiple of 12 hours, at that point its hands are back in the same position the true time shows. The first time this happens is when the watch has gained a full 12 hours = 720 minutes. Compute the time to gain 720 minutes. The watch gains 2 minutes of error per hour of real time. To accumulate 720 minutes of error: \frac{720 	ext{ minutes gained}}{2 	ext{ minutes gained per hour}} = 360…

The fast watch that is right again in 15 days

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