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# Exact times when hour and minute hand overlap ?

rehans oberoi
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Posts: 174
Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?

Zip Ped
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Posts: 336
22 times. Once every hour till 11 the hour hand is at 11 at which point they meet at 12.

Dave Trower
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Posts: 86
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.

Stan James
(instanceof Sidekick)
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Posts: 8791
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 ]