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?
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Hint
How many large pipes are required to drain the reservoir in 24 hours?
Answer
21 hours and 36 minutes.
Reasoning
Looking at the first clue:
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
Looking at the second clue:
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 (*), we know that in those 24 hours, 3 large pipes can drain 1 of those reservoirs.
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
multiply the hours by 9:
in 216 hours, 1 small pipe can drain 2 reservoirs
in 216 hours, 5 small pipes can drain 10 reservoirs
divide the hours by 10:
in 21.6 hours, 5 small pipes can drain 1 reservoir
21.6 hours = 21 hours and 36 minutes.
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