How many times do the minute and hour hands overlap in a 24-hour day?

How many times do the minute and hour hands overlap in a 24-hour day?

• A. 22
• B. 24
• C. 20
• D. 12

Answer: (A)

Think about how often the minute hand catches up to the hour hand. The minute hand moves 360 degrees per hour, while the hour hand moves 30 degrees per hour, so the relative speed is 330 degrees per hour (or 5.5 degrees per minute). To align, the minute hand must gain a full 360-degree lap on the hour hand, which takes 360 / 5.5 = 720/11 minutes ≈ 65.45 minutes. In 12 hours you get 12 hours worth of time divided by that interval: 12 hours is 720 minutes, and 720 ÷ (720/11) = 11 overlaps. In a full day (24 hours), that doubles to 22 overlaps.

Think about how often the minute hand catches up to the hour hand. The minute hand moves 360 degrees per hour, while the hour hand moves 30 degrees per hour, so the relative speed is 330 degrees per hour (or 5.5 degrees per minute). To align, the minute hand must gain a full 360-degree lap on the hour hand, which takes 360 / 5.5 = 720/11 minutes ≈ 65.45 minutes. In 12 hours you get 12 hours worth of time divided by that interval: 12 hours is 720 minutes, and 720 ÷ (720/11) = 11 overlaps. In a full day (24 hours), that doubles to 22 overlaps.