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The time is 7:05:27 (and .27 seconds)

Calculating by degree

Assume the minute hand doesn't move in steps ... it just glides continuously and analogly, at the rate of 6 degrees per minute. At 'M' minutes past the hour, it's pointing toward an azimuth of 6M degrees.

Assume the hour hand doesn't move in steps either; it also glides in a smooth analog fashion, at the rate of 30 degrees per hour. At 'M' minutes past 7:00, the hour hand points toward an azimuth of 210 + 30(M/60) = 210 + M/2 degrees. The direction opposite the hour hand is 180 degrees different, or 30 + M/2.

That's the direction we want the minute hand pointing.

6M = 30 + M/2

12M = 60 + M

11M = 60

M = 60/11 minutes = 5 minutes 27.27 seconds after 7:00.

Using this formula

The formula M = H * (60/11) gives the whole and decimal minutes past the hour for times that have overlapping hour and minute hands, where H is an hour between 1 and 10. Adding 6 hours to these times will provide the opposite times, except for 6 o'clock exactly (from 0:00:00).

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