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# A watch which gians uniformly is 5 minutes slow at 8:00 am

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Joined: 28 Jun 2004
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A watch which gians uniformly is 5 minutes slow at 8:00 am [#permalink]  18 Aug 2004, 15:26
A watch which gians uniformly is 5 minutes slow at 8:00 am on Sunday and is 5 min 48 seconds fast at 8:00 pm on the following Sunday. When did it show the correct time?
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Joined: 07 Jul 2004
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in 12 hours, it gained 10mins48seconds = 648 seconds
so each hour, it gains 54 seconds = 9/10 of a minute

So at 8am it is 300 seconds slower
9am, it will be 246seconds slower
10am, 192 seconds slower... etc. It will show the correct time when this difference reduces to 0.
For that to happens, it need to be 300/54 = 5 5/9 hours later. Which is about 1:30pm
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The clock gains 10 min 48 sec by 8 pm the FOLLOWING Sunday. That's 180 hours, or 10,800 minutes. That works out perfectly, since 10 min 48 sec is really 10.8 min, so when we divide, we see that the clock gets faster by 1 minute every 1000 minutes. Since it starts out 5 minutes slow, it'll be right on when it's gained 5 minutes, which is 1000x5=5000 minutes later.

5000 minutes is 3 days, 11 hours, and 20 minutes, which is Wed at 7:20PM.
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