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Topic: Clock
Message: Posted by: Steve Martin (Apr 1, 2004 07:05AM)
How many minutes and seconds past one o'clock are the hands on an analogue clock EXACTLY aligned?
Message: Posted by: Jonathan Townsend (Apr 1, 2004 12:16PM)
Good one... have to watch the moving target to get that one.
Message: Posted by: Mikey-Flys (Apr 1, 2004 12:39PM)
Is this a clock with a second hand or just a minute/hour hand? I haven't worked out the second hand yet but I think the hour/minute hand should be aligned 5 minutes and 27.27 seconds after comparing starting positions and relative velocities.

Of course, that is for a 12 hours clock face. A clock with 24 hour positions would take some more figuring :)
Message: Posted by: Steve Martin (Apr 2, 2004 05:15AM)
Well done, Mikey - that is correct.

I should have been a little more clear that I was ignoring the second hand - just considering the hour and minute hand.

For those who want to work it out, the easiest approach is to assume the hands start at one o'clock, then work out how many degrees of movement (of each hand) are represented by one minute. When the angles made by both hands are the same, you know the number of minutes that have passed. That number is 60/11 minutes (= 5 minutes and 27.27 seconds).