At noon the hour, minute, and second hands coincide. In about one hour and five minutes the minute and hour hands will coincide again.
What is the exact time (to the millisecond) when this occurs, and what angle will they form with the second hand?
(Assume that the clock hands move continuously.)

Answer

There are a few ways of solving this one. 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.

At noon the hour, minute, and second hands coincide. In about one hour and five minutes the minute and hour hands will coincide again.
What is the exact time (to the millisecond) when this occurs, and what angle will they form with the second hand?
(Assume that the clock hands move continuously.)

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