Treebeard's Stumper Answer 2 May 97

The countdown to Science Fair continues, so here's an easy clock stumper. At 12:00, the hour and minute hands of a clock point in exactly the same direction. How many times does this happen in a 12 hour period? The next meeting is not quite 1:05, since the hour hand moves a bit during those first 5 minutes. So exactly when do both hands meet, figured to the nearest second? Is there an easy way to work this out? *Bonus* How many working days are there until Science Fair? (Hint: May 9 at 5:00 at the Middle School for science, BBQ, and softball! The clock is ticking....)

The hour and minute hands of a clock meet exactly eleven times per twelve hour period, once per hour except for 11:00 to 11:59. 12/11 = 1.0909... = 1 hour 5 minutes and 27.2727... seconds. So the meeting times are:

  12:00:00  4:21:49   8:43:38
   1:05:27  5:27:16   9:49:05
   2:10:55  6:32:44  10:54:33
   3:16:22  7:38:11  12:00:00

That's m minutes past h hours when m = 60*h/11. So when are all three clock hands the closest together?

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