How many times during the day do the hands of a clock overlap? - Mathlete's Corner

How many times during the day do the hands of a clock overlap?
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?
From http://puzzles.nigelcoldwell.co.uk/thirtyfive.htm
Hour Hand = Minute Hand
      30t = 360t - 360
        t = 12(t - 1)
      11t = 12
        t = 12/11
          = 1.090909.... hours
          = 1h 5min 27.272727..seconds
In a 24 hour period, they would overlap 22 times.

The precise times they overlap (in hours) would be 12N/11: 1 + 1/11, 2 + 2/11, 3+ 3/11, all the way up to 11 + 11/11, which is 12 o'clock again.

Questions related to this:
Q. An analog clock is showing 2 o'clock right now. At what time will the hour and minute hands overlap next?
Q. What is the angle between the hour and minute hands at 4:10?

Also refer to http://www.mytechinterviews.com/clock-hands
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