At what time immediately prior to six o'clock are the hands of the clock exactly opposite to each other?
Give the exact time in hours, minutes and seconds.

The time taken, T, for a minute hand, traveling at 6 degrees per minute to travel exactly 360 degrees more than an hour hand (traveling at ½ degree per minute) is given by
6T + 360 = ½ T
T = 720/11 minutes. (1 hour 5 minutes 27 seconds (to the nearest second))
So every 720/11 minutes the hands are in exactly the same position, relative to each other.
So the hands were opposite, prior to 6 o clock, 720/11 minutes earlier
At 4:54 and 33 seconds

Posted by Lee on 2004-01-12 12:47:50