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A large fresh water reservoir has two types of drainage system: 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?

Answer: 21 hours and 36 minutes.

The exact size of the pipes and reservoir does not matter. If we label the large pipes L, the small pipes S and if the reservoir has a total of T litres, then:

T ÷ 6L = 12 which means L = T ÷ 72

and

T ÷ (3L + 9S) = 8 which means that S = T ÷ 108

we want

T ÷ 5S which gives 108 ÷ 5 hours = 21.6 hours = 21 hours and 36 minutes.

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