How many times in a half day the arrow of clock that show the minutes and arrow of clock that show the hours, match each other and in which time expressed in hours, minutes and seconds.
One is tempted to think that the hands meet every hour and 5 minutes: at 0:00, 1:05, 2:10, etc. However, this is incorrect, since by 1:05 the hour hand will have moved a bit forward and not exactly meet the minute hand. Also, that would give you the hands meeting at both 11:55 and 12:00, five minutes later, which is obviously wrong. It is that latter consideration that gives the key: the hands meet at 12:00, once between 1:00 and 2:00, once between 2:00 and 3:00, and so on, until they meet once between 10:00 and 11:00, and then do not meet again until 12:00. So the hands meet exactly eleven times.
Over 12 hours, the hands meet 11 times. Since the hands are moving at uniform speed, the interval of time between any two meets must be the same. So simply divide 12 hours by 11 to get the length of time between matches.