Hands of time!
10 hours, 9 min, 13 + 11/13 seconds
At 10 o'clock the minute hand is at 0 (zero).
Though the hour hand is at 10 it is, in effect,
at its zero point for solving the puzzle.
While the minute hand increases "x" minutes from zero,
the hour hand decreases "x/12" minutes from 10.
After x minutes the hands are symmetrical:
therefore the hour hand = minute hand
therefore 10 - x/12 = x
transposing 13x = 120
therefore x = 9 + 3/13 minutes
x = 9 min, 13 + 11/13 seconds.
Thus the hands are symmetrical at
10 hours, 9 min, 13 + 11/13 seconds.
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