When three pipes fill a pool, they can finish in 12 hours. Two of the pipes can finish in 18 hours if they are working together. How long would it take a third pipe to fill the pool on its own?

3 pipes take 12 hours
⇒ In 1 hour, the 3 pipes can fill 1/12 of the pool

2 of the pipes take 18 hours
⇒ in 1 hour, the 2 pipes can fill 1/18 of the pool

In 1 hour, the third pipe alone can fill :

[tex]\dfrac{1}{12} - \dfrac{1}{18} = \dfrac{3}{36} - \dfrac{2}{36} = \dfrac{1}{36} \text { of the pool}[/tex]

Time needed :

[tex]1 \div \dfrac{1}{36} = 1 \times 36 = 36 \text { hours} [/tex]

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Answer: It will take 36 hours for the third pipe to fill the pool.
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