Part II: how often does the minute hand pass the hour hand on an analog clock?
Answer:
Part I:
Every 60 mins, hour hand covers, 30 degrees
so for 15 mins, hour hand 7.5 degrees. which is the difference.
Part II:
consider the example of 1 past x at which they meet.
Let they meet at x degrees,
The minute hand covers 6 degrees every minute.
The hour hand covers 1/2 degree every minute.
6x-30 = x/2
11x = 60
x = 5 (5/11),
so they meet every 60 + 5.55555 minutes
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