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Puzzle Details

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.

In 12 hours: 6 large pipes can drain 1 reservoir.
In 24 hours: 6 large pipes can drain 2 reservoirs.
In 24 hours: 3 large pipes can drain 1 reservoir.        [1]

In 8 hours: 3 large + 9 small pipes can drain 1 reservoir.
In 24 hours: 3 large + 9 small pipes can drain 3 reservoirs.

But, by [1] we know that in those 24 hours 3 large pipes can drain 1 reservoir.

Therefore the other 2 reservoirs can be drained by the small pipes on their own:

In 24 hours: 9 small pipes can drain 2 reservoirs.

In 24 hours: 1 small pipe can drain 2/9 reservoirs.
In 216 hours: 1 small pipe can drain 2 reservoirs.
In 216 hours: 5 small pipes can drain 10 reservoirs.

Therefore 5 small pipes can drain 10 reservoirs in 216 hours.

216 hours ÷ 10 = 21.6 hours.

21.6 hours = 21 hours and 36 minutes.

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