On every clock we can see that at noon the hour, minute and second hand correctly overlay. In about one hour and five minutes the minute and hour hand will overlay again. Can you calculate the exact time (to a millisecond), when it will occur and what angle they will contain with second hand?

There are a few ways of solving this one. I like the following simple way of thinking.
The given situation (when the hour and minute hands overlay) occurs in 12 hours
exactly 11 times after the same time. So it’s easy to figure out that 1/11 of the clock
circle is at the time 1:05:27,273 and so the seconds hand is right on 27,273 seconds.
There is no problem proving that the angle between the hours hand and the seconds
hand is 131 degrees.

On every clock we can see that at noon the hour, minute and second hand correctly overlay. In about one hour and five minutes the minute and hour hand will overlay again. Can you calculate the exact time (to a millisecond), when it will occur and what angle they will contain with second hand?

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