### Brain Teasers

# Empty the Reservoir

Math
Math brain teasers require computations to solve.

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?

### Hint

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

21 hours and 36 minutes.Hide Hint Show Hint Hide Answer Show Answer

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## Comments

I'm not quite sure how you arrived at this answer.

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.

nice!

I'm going to assume that for the sake of your calculations, 23.6 = 21.6

nice one!

Better than most of these type of teasers.

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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