Assume that the hour and minute hands of a clock move without jerking. The clock shows a time between 8 o'cloc

Question

Assume that the hour and minute hands of a clock move without jerking. The clock shows a time between 8 o'clock and 9 o'clock. The two hands of the clock are one above the other. After how many minutes (nearest integer) will the two hands again be lying one above the other?

Accepted Answer

The minute hand gains 55 minutes on the hour hand every hour. For the hands to be one above the other (coincident), the minute hand must gain a full 360 degrees on the hour hand. This occurs approximately every 65.45 minutes. Since the question asks for the nearest integer and the coincidence happens after 8 o'clock, the time elapsed until the next coincidence will be after the 8:00 mark has passed. The hands coincide approximately at 8:43:38. The time until the next coincidence after that is approximately 65 minutes.