# Exact times when hour and minute hand overlap ?

rehans oberoi

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Zip Ped

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Dave Trower

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posted 9 years ago

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Let X be the number of the hour

Let t be the minutes passed the hour

So the time is X:t

Let h be the position of the hour hand

Let m be the position of the hour hand

h = X + t/60

m = t/5

Now time find where the two hands cross, we need to know when h = m

t/5 = X + t/60

12t = 60x +t

11t = 60x

t = 60X/11

For the first crossing, X =1

t = 60/11

t =5.45 minutes

t = 5 minutes and 27 seconds (note 27/60 is about 0.45)

So the first crossing is at 1:05:27

The second crossing is X =2.

t = 120/11

t= 10 minutes and 55 seconds

Second crossing at 2:10:55

By setting X to each hour you can solve for the remaining 9 crossing.

Let t be the minutes passed the hour

So the time is X:t

Let h be the position of the hour hand

Let m be the position of the hour hand

h = X + t/60

m = t/5

Now time find where the two hands cross, we need to know when h = m

t/5 = X + t/60

12t = 60x +t

11t = 60x

t = 60X/11

For the first crossing, X =1

t = 60/11

t =5.45 minutes

t = 5 minutes and 27 seconds (note 27/60 is about 0.45)

So the first crossing is at 1:05:27

The second crossing is X =2.

t = 120/11

t= 10 minutes and 55 seconds

Second crossing at 2:10:55

By setting X to each hour you can solve for the remaining 9 crossing.

Stan James

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posted 9 years ago

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I got the same answer, I think the same way. The hands cross 11 times in 12 hours = every 12/11 of an hour = every 1:05:27.27...

[ March 12, 2006: Message edited by: Stan James ]

[ March 12, 2006: Message edited by: Stan James ]

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