Mathematics Question Involving Watches

[Shore Guy]

There is a question whose solution eluded me for years. I occasionally revisited it over time only to be frustrated by not succeeding to solve it by brute force and giving up after a few minutes. Then one night after retiring to bed and revisiting it again, I solved it in 10 or so seconds, without paper and pencil which I never take to bed with me (I'm not that crazy.)

The question is:

Determine between 12 noon and 12 midnight, the EXACT times that the minute and hour hands coincide. Express the answers as hours and fractions of hours beyond 12 noon.

I will give the solution and proof in this thread in a few weeks after allowing members to ponder this. This can be done in two or three lines. When you see the solution, you will say to yourself, why didn't I think of that!

If any member comes up with this elegant (and really beautiful proof), I will recognize it. I will not comment or even look at a number crunching or brute force attempt, valid or invalid.