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Find the time between two and three o'clock that the minute hand and hour hand of a clock are diametrically opposite.

 Oct 16, 2020
 #1
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Hour hand starts at 60 degrees and moves 1/2 degree per minute  1/120 degree per sec

  minute hand moves 1/10 degree per second

 

60 + 1/120 x    =   1/10 x  -180  

240 + 1/120 x = 1/10 x 

240 = 1/10 x - 1/120 x

240 =  12/120 x = 1/120 x

240 = 11/120 x

x = 2618.18 seconds after 2 o'clock

 

minute hand will be at   43.63 minutes  =  43:38

 

  ~ 2 : 43 : 38

 
 Oct 16, 2020
edited by ElectricPavlov  Oct 16, 2020
edited by ElectricPavlov  Oct 16, 2020
 #2
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180=abs((30*2) - (5.5*M)), solve for M

 

M = 480 / 11 =43.636363.....

 

Time =2:43:38

 
 Oct 16, 2020

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