Minus' Solution to
Posted April 14 - 20, 1997
Minus' Solution to
When the slow clock has progressed 12 hours, the real time
will have progressed 24 hours. Both will be the same. Every
12 hours the slow clock and the real time will be the same.
Therefore, both the fast clock and the slow clock will be
correct every 24 hours. Since both are correct with the real time
at Dec. 1 at 1 minute after midnight, they will be correct at
1 minute after midnight on Dec. 2, 3 . . ., and 31. Both
clocks will be correct at the same time 31 times in the month.
When real time has progressed 12 hours, the fast clock will
have progressed 18 hours. When real time has progressed 24
hours, the fast clock will have progressed 36 hours, which
will make the real time and the fast clock the same every 24 hours.
David He, a sixth grader, teased our hungry mascot with an answer, but no solution. Oh well, Minus has been trying to slim down anyways.
The answer for this week's math challenge is 31.Thanks.
Mr. T and his Little Einsteins, in sweltering Texas, came through (as always) with their algebraic wonder of the week. Nice of y'all to keep our poor mascot from starving. Hope Mr. T drives golf balls as straight and far as he does his students!
We determined that the only way either of the clocks could display the correct time was for the clock and actual time to be exactly 12 hours apart, thus appearing to be the same on a 12-hour clock. Therefore since the fast clock (Clock F) is running at a 3/2 ratio to actual time, the simple algebraic proportion:
(T + 12)/ T = 3/2 Solving for T we get T= 24 hours, meaning that the times will be exactly 12 hours apart and thus the same on a 12-hour clock, every 24 hours.
Following the same procedure with the slow clock (Clock S), we found it to be running at a rate of 1/2 the actual time and also becoming "correct" when it was exactly 12 hours slow, producing the proportion:
(T - 12)/T = 1/2 Solving for T we find that lo and behold, this too will occur every 24 hours. So, since the clocks started correct on December 1st and became correct again every 24 hours, then the two clocks would both be correct at the same time at 00:01:00 each and every of the 31 mornings in December. ANSWER = 31 TIMES IN DECEMBER.
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