The minute-hand and second-hand of a clock cross each other _______ times between 09:15:00 AM and 09:45:00 AM on a day.
30
At 09:15:00 the minute hand is 90 degrees ahead of the second hand. Their relative angular speed is 6 − 0.1 = 5.9 degrees/s. Crossings occur at \(t_k=(90+360k)/5.9\) seconds after 09:15. The condition \(0\lt t_k\lt 1800\) gives k = 0, 1, …, 29: 30 crossings.
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