Al sent me another clock problem, so I will put it here, and then to keep a little space between the problem and the answer, (for those who try to solve it themselves) I will post a joke that Jeannie sent me today at work...

First, the problem...How long after 7:00 will the second hand bisect the angle formed by the other two hands?

and now to distract you, a joke:

"While walking along the sidewalk in front of his church, our minister heard the intoning of a prayer that nearly made his collar wilt. Apparently, his 5-year-old son and his playmates had found a dead robin. Feeling that proper burial should be performed, they had secured a small box and cotton batting, then dug a hole and made ready for the disposal of the deceased.

The minister's son was chosen to say the appropriate prayers and with sonorous dignity intoned his version of what he thought his father always said: 'Glory be unto the Faaather, and unto the Sonnn , and into the hole he goooes.' "

It reminds me of when my grandaughter was young and would sob "It's not there!" when she didn't get her way... meaning, of course, "It's not FAIR."...

OK, here is my attempt at the solution: The hour hand starts at 210 degrees and moves 1/120 degrees per second... The minute hand starts at zero degrees and moves at 1/10 degree per second; and the second hand moves at 6 degrees per second from a zero degree start.

When the second hand bisects the other two, the angle between the hour and second hand will equal the angle between the second and minute hand (with the second hand in the middle)...

so I set hour-second = second - minute or...

210 + 1/120 T (in seconds) - 6T = 6T- 1/10 T and simplify to get

210 - 719/120 T = 59/10 T and collect T on right side to get

210 = 1427/120 T multiply by the reciprocal of the coefficient of T and

T= 17.6594 seconds afer 7 o'clock...

Checking the angles,, the hour hand is at 210.1471619 degrees amd the minute hand is at 1.76594 degrees, with the second hand at 105.9565522 degrees...The angle between hour and second is 210.147-105.957 = 104.19.......the hour between second and minute is 105.957-1.766 = 104.191... I'm calling that a winner...

Ok, for a second try... do the same thing on a 24 hour clock....