+77 Find the time between one and two o'clock that the minute hand and hour hand of a clock are diametrically opposite.
+223 180 = 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.
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.
