Question 1197924: At exactly 12 o'clock noon the hour hand of a clock begins to move at twelve times its normal speed, and the minute hand begins to move backward at twice its normal speed. When the two hands next coincide, what will be the correct time?
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
The normal speed of the hour hand is 360 degrees in 12 hours, or 30 degrees per hour, or 1/2 degree per minute. So the speed of the hour hand of this clock starting at noon is 12*(1/2) = 6 degrees per minute.
The normal speed of the minute hand is 360 degrees in 1 hours, or 6 degrees per minute, so the speed of the minute hand of this clock starting at noon is 12 degrees per minute.
Since the hands are moving in opposite directions starting at noon, they are moving towards each other at the rate of 6+12 = 18 degrees per minute.
The hands will coincide when they have moved towards each other a total of 360 degrees; at 18 degrees per minute, that will take 360/18 = 20 minutes.
So the two hands will coincide 20 minutes after noon, at 12:20 pm.
ANSWER: 12:20 pm
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