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Switching Hands (Posted on 2009-04-25) Difficulty: 2 of 5
It was some time between 7 and 8 PM that Sam looked at his watch. Some time later, between 10 and 11 PM, he looked again, and coincidentally, the hour hand and minute hand were exactly switched from the first time he looked. What were the two times?

  Submitted by Charlie    
Rating: 3.0000 (1 votes)
Solution: (Hide)
Let the times be x minutes past 7 and y minutes past 10.

For ease of calculation let's represent angular positions on the face of the clock as hour-equivalents.

At the earlier time, the hour hand is on 7 + x/60 and the minute hand is on x/5.

At the later time, the hour hand is on 10 + y/60 and the minute hand on y/5.

From the puzzle,

7 + x/60 = y/5
10 + y/60 = x/5

(420 + x) / 60 = y/5

60y = 2100 + 5x

12y = 420 + x

x = 12y - 420

Substituting in the 12x = 600 + y derived from the other equation:
144y - 5040 = 600 + y

143y = 5640

y = 5640/143

It follows that x = 7620/143

To the nearest second, the times are 7:53:17 and 10:39:26.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre: SolutionRosy2009-04-27 14:16:35
SolutionHarry2009-04-25 17:29:56
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