At noon and midnight the hour and minute hands are exactly coincident with each other. How many other times between noon and midnight do the hour and minute hands cross?
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8
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9
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10
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11
The hour and minute hands coincide 11 times in every 12-hour period, including at noon (12:00) and at midnight (12:00). Between these two endpoints, they cross at approximately 1:05, 2:11, 3:16, 4:22, 5:27, 6:33, 7:38, 8:44, 9:49, and 10:55, which gives us 10 times. The hands move continuously, creating these crossing points approximately every 65.45 minutes.
To answer this question, let's analyze the movement of the hour and minute hands on a clock.
The minute hand completes a full revolution every 60 minutes, while the hour hand completes a full revolution every 12 hours. Therefore, for every hour, the minute hand moves 12 times faster than the hour hand.
Let's consider a scenario where the minute hand is ahead of the hour hand, and they are about to cross each other. As time passes, the minute hand continues to move ahead, while the hour hand slowly catches up. Eventually, they will cross each other, and the minute hand will be behind the hour hand.
The only times when the minute and hour hands cross each other between noon and midnight are when the minute hand is ahead of the hour hand. From noon to 1 o'clock, the minute hand crosses the hour hand once. From 1 o'clock to 2 o'clock, the minute hand crosses the hour hand twice. This pattern continues until 11 o'clock, where the minute hand crosses the hour hand 11 times.
Therefore, the correct answer is C) 10. The hour and minute hands cross each other 10 times between noon and midnight.