We all know that the hour hand and the minute hand on a clock travel at diff speeds. However, there r certain occasions when they r exactly opposite each other. Can u give a simple formula for calculating the times of these occasions?

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Francis

  • Oct 10th, 2006
 

Hi,I am familiar in relative speed with trains. So let me change this problem in terms of relative speed.Let the distance be the degree in the clock i.e. between 0 to 360 degreesTherefore the speed of the hour hand is 30 degrees per hour that is 0.5 degrees per miinute.Speed of the minute hand is 360 degrees per hour that is 6 degrees per minute.So in any problem initail time will be given Using that calculate the number of degrees the minute hand should travel to reach the opposite direction. Then find the time taken to cover those degrees using the minute hand's relative speed.Is that clear,Thanks,Francis

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go2francis

  • Oct 10th, 2006
 

Hi,I am familiar in Relative speed with trains.So let me change this problem to a relatve speed problem.Let the distance be the degrees covered in the clock.Then the speed of the hour hand is 30 degrees per hour.The speed of the minute hand is 360 degrees per hour.In any problem the initial time will be given. With that the number of degrees the minute hand should cover to reach the opposite side can be calculated. Then the time taken to cover those degrees by the minute hand can be calculated using the relative speed.Is that clear?If the answer is repeated .... then sorry friends.Thanks,Francis

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Rathinavelu

  • Oct 23rd, 2006
 

The equation is

 M = (360 + 60H)/11

 H = 0 ( for 12 pm/am),1( for 1pm/am),2,3,4......11

H - Hour; M - Minute

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shashank_tangwan

  • Mar 1st, 2007
 

I think its very simple just a matter of relative speeds.

Hour hand --> 30 degrees /hr (i.e. 5/60 * 360)

Min hand --> 360 degrees / hr (one whole circle)

Rel . speed (r.s.) = 360-30=330 degrees / hr.

So for the hands to be opposite to each other , separation = 180 degrees

Now time taken for this is= separation/ r.s.= 180/330=6/11 hours=32 & 8/11 minutes


Hence the hands will be opposite to each other every 32 & 11/8 minutes

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shashank_tangwan

  • Mar 1st, 2007
 

CORRECTION :

There is a discrepancy of 5/11 mins in overlapping and it gains by this much time in 65 mins ..................  Which means that :

correct clock takes 65 & 5/11 mins to overlap where this one takes 65 mins

so ,
 
correct clock takes 60 mins to complete an hour  while this one takes 59 & 7/12 mins


hence the actual gain / hr is  ---> 60 - (59 + 7/12) = 5/12 mins...

Hence the actual gain per hour  is 5/12 mins  & Not 5/11 mins

P.S. --> Please ignore my earlier post (which is incorrect), it was a hasty reply. My apologies

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Rishi_143love

  • Jul 25th, 2008
 

For exactly oppodite orientations,the angle between the must be an odd multiple of"pi"
Now,angular speed of minute hand=2pi             rad/hour

        angular speed of hour hane    =2pi/12       rad/hour
Let T be the time in hour when they are oppsite

Therefore,in time T

        displacement of minute hand=(2pi)T           rad

        displacement of hour hand    =(2pi/12)T     rad


Therefore,
                 2(pi)T-2(pi)T/12   =   (2n+1)(pi)
                 2T-T/6=2n+1
                 11T/6=2n+1
                 T=(2n+1)*6/11,  where n=1,2,3........

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