+101 At exactly 12 o'clock noon the hour hand of a clock begins to move at 2 times its normal speed, and the minute hand begins to move backwards at half its normal speed. When the two hands next coincide, what will be the correct time?
Hour hand usually moves at .5 degree per minute.....now it is at 1 degree per minute
Minute hand usually moves at 6 degrees per minute now moving retrograde at 3 degrees per minute
Starting at 12 o'clock as zero degrees
minute hand position = 360 - 3 * m
hour hand position = 1 * m
equate them 360 - 3m = m
360 = 4m
m = 90 minutes when they meet which will 13:30 correct time
( however , when they meet it will show ~ 15:15 )
