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.

Answer: The hands of the clock are opposite each other at 4:54 and 33 seconds.

Explanation:

The minute hand moves 360 degrees/hour
= 1/10 degree/second. The hour hand moves 360 degrees/12 hours = 1/120 of a degree/second. At 4 o'clock, the minute hand is straight up (zero degrees), and the hour hand is at the 4 (120 degrees). T seconds after 4 o'clock, the minute hand is at T/10 degrees and the hour hand is at (120 + T/120) degrees, and the angle between them is
T/10 - (120 + T/120). When they are pointing in opposite directions, this angle is 180 degrees.

180 = T/10 - (120 + T/120)

T = 3273 seconds = 54 minutes + 33 seconds

So the hands are opposite each other, 54 minutes and 33 seconds after 4:00.

Edited on January 12, 2004, 9:58 am

Posted by Penny on 2004-01-12 09:54:19