Question

In a period of 12 hours, how many times will the hands of a clock be making an angle of 180 degrees?

Answer 1

For every 180 degrees that the minute hand gains on the hour hand there will be one 90 degree angle, so every 49 1/11 - 16 4/11 = 32 8/11 minutes.
24 hours is 1440 minutes. 1440/(32 8/11 ) = 44.
So every 24 hours there are 44 right angles between minute hand and second hand.

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