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Puzzle:
"How many degrees (if any) are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?
What is the first time after 3pm when the hour and minute hands of a clock are exactly on top of each other?"
- We can easily determine the relationship between the speed of the hour and minute hands (in degrees):
- hour hand: (360 / 12) / 60 = 0.5 degree per min.
- minute hand: 360 / 60 = 6 degree per min.
- When the time is a quarter past three:
- hour hand (in degrees): 90 + 0.5 * 15 = 97.5 degrees.
- minute hand (in degrees): 15*6 = 90 degrees.
- their difference: 7.5 degrees.
- We can generalize the formula for solving the second problem:
- let's time after 3 pm be t in minutes.
