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Gertrude and her grandmother's clocks

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Gertrude and her grandmother's clocks [#permalink] New post 05 Feb 2009, 13:13
Gertrude and her grandmother have 2 clocks with 12 digits.

the 1st clock loses 3 minutes every hour. It will show that 57 minutes have elapsed when in fact exactly one hour has gone by.

The second clock gains 5 minutes every hour. It will show that 65 minutes have elapsed when in fact one hour has gone by.

Gertrude and grandmother always open a bottle of champain when 2 clocks strike the correct time of 12 at midnight on the same night.

Last night they opened a bottle of champain.

How many full days must go by before they may do so again?
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Re: Gertrude and her grandmother's clocks [#permalink] New post 05 Feb 2009, 17:53
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60 days

1st clock: -3 min per hour ---> 3/60=1/20. This means that every 20 days 1st clock has 1 day (24 hours) delay.
2nd clock: +5 min per hour ---> 5/60=1/12. This means that every 12 days 2nd clock has 1 additional day (24 hours).

These two cycles coincide at at LCM(12,20)=60
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Re: Gertrude and her grandmother's clocks [#permalink] New post 06 Feb 2009, 07:59
walker wrote:
60 days

1st clock: -3 min per hour ---> 3/60=1/20. This means that every 20 days 1st clock has 1 day (24 hours) delay.
2nd clock: +5 min per hour ---> 5/60=1/12. This means that every 12 days 2nd clock has 1 additional day (24 hours).

These two cycles coincide at at LCM(12,20)=60


great explanation!! Mr biker.
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Re: Gertrude and her grandmother's clocks   [#permalink] 06 Feb 2009, 07:59
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