 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Switching Hands (Posted on 2009-04-25) 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. Subject Author Date re: Solution Rosy 2009-04-27 14:16:35 Solution Harry 2009-04-25 17:29:56 Please log in:

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