In T hours, the minute hand completes T laps ( Where T is any natural number). In the same amount of time, the hour hand completes T/12 laps.For example in 1 hr minute and completes 1 lap and hour hand completes 1/12 lap. I hope this is clear so far.
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.
Since we have 24 hours in a day, we can solve the above equation for N , 24 = 24/12 + N
24 = 2 + N
N = 22
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.
Since we have 24 hours in a day, we can solve the above equation for N , 24 = 24/12 + N
24 = 2 + N
N = 22
Great post.
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