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Time, Clock & Calendar Medium 3 min

A clock shows exactly 3:00. At what exact time between 3:00 and 4:00 will the hour and minute hands overlap?

Hint
The minute hand gains 55 minutes of angular movement on the hour hand every hour.

Answer

Approximately 3:16:21.8.

Explanation

At 3:00 the hands are 90 degrees apart. The relative speed is 5.5 degrees per minute. Therefore the required time is 90 / 5.5 = 16.3636 minutes.

Step-by-Step Solution

90 ÷ 5.5 = 16.3636 minutes.
0.3636 × 60 = 21.8 seconds.
Therefore the hands overlap at approximately 3:16:21.8.
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