Time Please (Posted on 2004-01-12)

	Submitted by Ravi Raja
Rating: 2.6667 (3 votes)
Solution:	(Hide)
It is obvious that between 5 O'clock and 6 O'clock the hands will not be exactly opposite to each other. It is also obvious that the hands will be opposite to each other just before 5 O'clock. Now to find exact time: The hour hand moves 1 degree for every 12 degrees that the minute hand moves. Let the hour hand be X degree away from 5 O'clock. Therefore the minute hand is 12X degree away from 12 O'clock. Therefore solving for X Angle between minute hand and 12 O'clock + Angle between 12 O'clock and 4 O'clock + Angle between 4 O'clock and hour hand = 180 12X + 120 + (30-X) = 180 11X = 30 Hence X = 30/11 degrees (hour hand is X degree away from 5 O'clock) Now each degree the hour hand moves is 2 minutes. Therefore minutes are = 2 * 30/11 = 60/11 = 5.45 (means 5 minutes 27.16 seconds) Therefore the exact time at which the hands are opposite to each other is = 4 hrs. 54 min. 32.74 seconds.

	Subject	Author	Date
	Puzzle Solution	K Sengupta	2022-01-03 21:25:56
	problem solution	K Sengupta	2007-03-30 05:19:42
	umm	paul	2004-03-24 22:34:03
	question	Inferno	2004-02-05 23:59:58
	Yet another answer	P C	2004-02-04 22:17:36
	Different Answer	Richard	2004-01-12 23:58:20
	working backwards	Lee	2004-01-12 12:47:50
	Full Solution	np_rt	2004-01-12 10:36:01
	Solution	Penny	2004-01-12 09:54:19