In-a-swimming-pool-there-are-four-pipes-that-fill-it-with-water-When-pipes-1-2-3-work-the-pool-fills-in-12-minutes-When-pipes-2-3-4-work-the-pool-fills-in-15-minutes-When-pipes-1-and-4-work

Question Number 199632 by hardmath last updated on 06/Nov/23

In a swimming pool there are four pipes that fill it with water. When pipes 1, 2, 3 work, the pool fills in 12 minutes. When pipes 2, 3, 4 work, the pool fills in 15 minutes. When pipes 1 and 4 work, the pool fills in 20 minutes. Find how many minutes the pool fills if all four pipes work simultaneously.

Answered by AST last updated on 06/Nov/23

$$Letvolumeofpoolbea;speedofpipes1,2,3,4$$$$bew,x,y,z\left(vol/min\right)\Rightarrow w+x+y=\frac{a}{12}\dots \left(i\right)$$$$x+y+z=\frac{a}{15}\dots \left(ii\right);w+z=\frac{a}{20}\dots \left(iii\right);$$$$\left(i\right)-\left(ii\right)\Rightarrow w-z=\frac{a}{60}\Rightarrow 2w=\frac{4a}{60}\Rightarrow w=\frac{a}{30}$$$$\Rightarrow x+y=\frac{a}{20}\Rightarrow w+x+y+z=\frac{a}{10}$$$$\Rightarrow Allpipeswillfillin10minutes$$

Commented by hardmath last updated on 06/Nov/23

$$\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}\mathrm{prafessor}$$

Answered by mr W last updated on 06/Nov/23

$$2/(1/12+1/15+1/20)=10minutes$$

Commented by hardmath last updated on 06/Nov/23

$$\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}\mathrm{my}\mathrm{dear}\mathrm{professor}$$

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