show that the hour hand and the minute hand overlaps 22 times a day
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Did you think the answer was 24 times? Well if you did, it’s time you think again. Let’s do some math.
In T hours, the minute hand completes T laps. In the same amount of time, the hour hand completes T/12 laps.
The first time the minute and hour hands overlap, the minute hand would have completed 1 lap more than the hour hand. So we have T = T/12 + 1. This implies that the first overlap happens after T = 12/11 hours (~1:05 am). Similarly, the second time they overlap, the minute hand would have completed two more laps than the hour hand. So for N overlaps, we have T = T/12 + N.
In T hours, the minute hand completes T laps. In the same amount of time, the hour hand completes T/12 laps.
The first time the minute and hour hands overlap, the minute hand would have completed 1 lap more than the hour hand. So we have T = T/12 + 1. This implies that the first overlap happens after T = 12/11 hours (~1:05 am). Similarly, the second time they overlap, the minute hand would have completed two more laps than the hour hand. So for N overlaps, we have T = T/12 + N.
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Hello dear your answer is in down...
I don't want to make the answer lendy....so it's in short...
the final equation is than:60N%60=0.5N,N€[0,720).
there are 11 distance solution to this equation in the selected range.show the hand overlap 11 times in each 12 hours period.job for the overlap 22 times in its day..
I don't want to make the answer lendy....so it's in short...
the final equation is than:60N%60=0.5N,N€[0,720).
there are 11 distance solution to this equation in the selected range.show the hand overlap 11 times in each 12 hours period.job for the overlap 22 times in its day..
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