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At exactly 12 o'clock noon the hour hand of a clock begins to move at six times its normal speed, and the minute hand begins to move backwards at five-sixths its normal speed. When the two hands next coincide, what will be the correct time?

 Oct 25, 2019
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When you say "coincide", do you mean when they are "on top of each other?".

 

If that is what you mean, then:

Every minute on a regular Clock, the hour-hand moves forward 1/2 minute, while the minute-hand moves backwords 5/6 minute.....So, since they are moving towards each other then:

1/2m + 5/6m =60 minutes.

Solve for m and m = 45 minutes(on a regular Clock).

So, the hour-hand will be: 1/2 x 45 =22.5 minutes on your faulty Clock. And:

5/6 x 45 =37.5 minutes (backwards) for the minute-hand. Or: 60 - 37.50 =22.50 when both hands will be on top of each other.

So 45 minutes will have passed on a regular Clock, or the time will be:12:45 pm.

 Oct 25, 2019

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