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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?

 Oct 17, 2021
 #1
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12:45

 Oct 17, 2021
 #2
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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 )

 Oct 17, 2021

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