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Time, Clock & Calendar Medium 3 min

How many times do the hour and minute hands overlap in a 12-hour period?

Hint
They do not overlap exactly once every hour.

Answer

11 times.

Explanation

The minute hand gains 360 degrees on the hour hand every 65 5/11 minutes. During 12 hours, the hands meet 11 times.

Step-by-Step Solution

Relative angular speed = 5.5° per minute.
12 hours = 720 minutes.
720 ÷ (360/5.5) = 11.
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