Between 7 and 8 o'clock, the dashed 12–6 line will exactly bisect the angle between the two hands, so the hands look mirror-symmetric about it. At what time does this happen?

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Accepted Answer

23 1/13 min past 7. Symmetry about the 12–6 line means the two hands' angles from 12 add up to 360^°: (210+ m2)+6m=360, so 6.5m=150 and m= 30013=23 113. (25 min ignores the hour hand's movement; 23 111 divides by 11 out of habit — here the hands' speeds ADD, 6+0.5=6.5.)

Between 7 and 8 o'clock, the dashed 12–6 line will exactly bisect the angle between the two hands, so the hands look mirror-symmetric about it. At what time does this happen?

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