The clock puzzle Answer

The hands are directly opposed at 6:00 sharp.  They are opposed again a little after 7:05, a little after 8:10; 11 times in 12 hours.  Therefore, the time between each is 12/11 or 1 & 1/11 hours. This works out to 1 hr 5 min 27 & 3/11 seconds.
6:00
7:05:27 & 3/11
8:10:54 & 6/11
9:16:21 & 9/11
10:21:49 & 1/11
11:27:16 & 4/11
12:32:43 & 7/11
1:38:10 & 10/11
2:43:38 & 2/11
3:49:05 & 5/11
4:54:32 & 8/11
6:00:00

Looking at the second hand in the picture gives us the answer of 10:21:49 & 1/11

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