When do the hands meet between 5 and 6 o'clock?

Question

Somewhere between 5:00 and 6:00 the minute hand catches up with the hour hand and the two point in exactly the same direction. At what exact time does this happen? Give the answer to the nearest second, or as an exact fraction of a minute past five.

Accepted Answer

At 5:27 and 3/11 minutes, which is about 5:27:16. Setting it up. At 5:00 the hour hand points at 150 degrees (5 × 30) and the minute hand at 0 degrees. Every minute, the minute hand moves 6 degrees and the hour hand moves 0.5 degrees, so the minute hand gains 5.5 degrees per minute on the hour hand. Solving. The gap of 150 degrees closes at 5.5 degrees per minute, so it takes 150 / 5.5 = 300/11 minutes, which is 27 and 3/11 minutes. Three elevenths of a minute is about 16.4 seconds. So the hands meet at 5:27:16 roughly. A cross-check with the 11-laps idea. The hands coincide 11 times in 12 ho…

When do the hands meet between 5 and 6 o'clock?

Your answer

Discussion

Learn the concepts

Related questions