Question

The minute hand of a church clock is twice as long as the hour hand. After what time after midnight does the end of minute hand move away from the end of the hour hand at the fastest rate A) 11 minutes past midnight C) 32 minutes past midnight B) 21 minutes past midnight D) 47 minutes past midnight
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Answer #1

Using the constant angular speed of the two hands in radians per minute ωm = 2 π / 60 and ωh = 2 π / 12 × 60

one get the time at which the speed difference is at a maximum θm − θh = π

( ωm − ωh ) tmax = π

which gives the required configuration of the clock hands 32 minutes 44 seconds after midnight.

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