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a leak in bottom

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a leak in bottom

by sanju09 » Mon Apr 06, 2009 4:21 am
A cistern is filled by an inlet valve in 5 hours. However because of a leak in bottom, it takes 30 minutes more to fill up. In how much time will the leak empty the filled cistern independently?
A. 5.5 hours
B. 55/21 hours
C. 55 hours
D. 11 hours
E. 50 hours
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by tacosychelas » Mon Apr 06, 2009 4:52 am
C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55
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by rossmj » Mon Apr 06, 2009 2:20 pm
I get E. 50 hours.

The rate the tank is being filled is 1tank/5hours or 1tank/300min the time is 5.5 hrs or 330 min. So 10% longer than it should have taken. So the rate the tank is leaking would be 1/10th the rate it is being filled or 1tank/3000mins or 1tank/50hours.

Please correct me if I'm wrong and let me know where my logic failed.
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by logitech » Mon Apr 06, 2009 2:58 pm
tacosychelas wrote:C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55
Great solution.

5X=5.5(X-Y)

X=11Y

So 5 hrs vs 55 hrs
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by dtweah » Mon Apr 06, 2009 6:01 pm
tacosychelas wrote:C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55
Good soln Logit. For formula or algebra haters just do

1/5 -1/5.5= 1/55. (TAke the difference between per hour work done without and with the leak and you get the per hour work done by the leak)
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