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The hands of a clock (Posted on 2002-05-23) Difficulty: 2 of 5
Anne and Mike have an argument about the hands of the clock:

Anne: "The minute hand takes one hour to make a complete circle. Therefore, it will pass the hour hand once every hour!"

Mike: "But by the time the minute hand has made a full circle, the hour hand will have moved 1/12th of the circle ahead. And by the time the minute hand gets to that spot, the hour hand will have moved forward yet again. This will continue indefinitely, so it is obvious that contrary to what it may seem like, the minute hand will never pass the hour hand."

In reality, how often does the minute hand pass the hour hand?

  Submitted by levik    
Rating: 3.3636 (11 votes)
Solution: (Hide)
The hour hand takes 12 hours to make a full revolution around the face of the clock. The minute hand will have made 12 revolutions in that period of time, so it must have overtaken the hour hand (12 - 1 = 11) times.

Since the hands are moving at a constant rate, each period between the clock hands' meeting is equal, and therefore they take place 12 hours / 11 times = 12/11th of an hour apart. (This is roughly 66 minutes, but you can calculate it exactly if you wish.)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle Solution: Method IIK Sengupta2008-05-19 05:48:10
SolutionPuzzle Solution: Method IK Sengupta2008-05-19 05:47:04
AnswerK Sengupta2008-03-15 04:01:57
8th Grade ISATTim Campbell2005-12-27 04:48:58
SolutionNo SubjectSteven Lu2004-12-06 01:29:04
SolutionAchilles and the Tortoise !!!!!!!!!Penny2003-12-17 02:58:17
re: solutionPopstar Dave2003-09-08 09:42:35
solutionFatBoy2003-09-03 10:19:19
And in more detail...Jim C2003-06-05 09:33:32
Solutionquite easy really....Matthew Bobbins2002-12-15 10:18:18
Hmm...Gautam Joshi2002-12-04 01:14:34
re: my solutionHope2002-08-18 17:00:17
my solutionshaun2002-06-12 02:39:26
SolutionSimple counting.TomM2002-05-23 13:29:24
SolutionEnder2002-05-23 04:27:41
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