Find the time between one and two o'clock that the minute hand and hour hand of a clock are diametrically opposite.
180 = T/10 - (60 + T/120) If you solve the equation for T, you'll know how many seconds after the hour it takes to move the two hands to opposite directions.
Source of above formula: http://mathforum.org/library/drmath/view/56835.html
The above formula works only for hours between 2 and 3 O'clock. To make it work for hours between 1 and 2 O'clock, we must adjust it as follows: 180 = T/10 - (30 + T/120), which changes the number of degrees from 60 for 2 O'clock to 30 degrees for 1 O'clock. So now, if we solve for T in the above formula, we get T =25,200 / 11 seconds after 1 O'clock, or 2,290.9090......seconds, or 38.181818... minutes after 1 O'clock when the 2 hands will be exacly opposite each other, or 180 degrees apart.
So the time will be 1:38:~11. And that is the exact time.