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Empty the Reservoir

Math brain teasers require computations to solve.

 

Puzzle ID:#1401
Fun:*** (2.33)
Difficulty:** (1.92)
Category:Math
Submitted By:psychodude57****
Corrected By:shogun

 

 

 



A large fresh water reservoir has two types of drainage systems, small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours. How long will 5 small pipes, on their own, take to drain the reservoir?

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Hint

The exact sizes of the pipes and reservoir do not matter.
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Comments

wchstennis
Dec 27, 2001

I'm not quite sure how you arrived at this answer.
ymiroc
Jun 11, 2002

Here is the explanation. If 6 large pipes can drain it in 12 hours, then a single large pipe can drain it in 72 hours. In other words a large pipe drains 1/72 of the resevoir every hour. Additionally, in 8 hours, we are told, 9 small pipes and 3 large pipes can drain it. The three large pipes must have drained 24/72 of the resevoir( 8*3*(1/72)). Thus 9 small pipes must drain the remaining 48/72, or 2/3, of the resevoir in 8 hours. In other words a single small pipe can drain 2/3 in 72 hours. If a small pipe drains 2/3 in 72 hours, it drains the whole resevoir in 108 hours. We can now answer the question: 5 small pipes drain 5/108 of the resevoir each hour. It will therefore take 23.6 hours for the five pipes to drain the resevoir.
paul726Aus*
Mar 05, 2006

nice!
Smudgeza*
Jun 18, 2006

I'm going to assume that for the sake of your calculations, 23.6 = 21.6
tonjawithaj*us*
Jul 31, 2006

nice one!
javaguru*us*
Feb 06, 2009

Better than most of these type of teasers.
Jimbo*au*
Apr 15, 2009

I just assumed that the reservoir contained 720 gigalitres and went from there (pick a number easily divisible by all of the 8s , 9s, etc). This tells you that a large pipe drains at a rate of 10 gigalitres per hour etc. Good teaser.

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