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.


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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 deleteduser1 last updated on 06/Nov/23

	$L e t v o l u m e o f p o o l b e a; s p e e d o f p i p e s 1, 2, 3, 4$ $b e w, x, y, z (v o l / m i n) \Rightarrow w + x + y = \frac{a}{12} . . . (i)$ $x + y + z = \frac{a}{15} . . . (i i); w + z = \frac{a}{20} . . . (i i i);$ $(i) - (i i) \Rightarrow w - z = \frac{a}{60} \Rightarrow 2 w = \frac{4 a}{60} \Rightarrow w = \frac{a}{30}$ $\Rightarrow x + y = \frac{a}{20} \Rightarrow w + x + y + z = \frac{a}{10}$ $\Rightarrow A l l p i p e s w i l l f i l l i n 10 m i n u t e s$
	Commented by hardmath last updated on 06/Nov/23

	$thank you so much prafessor$
	Answered by mr W last updated on 06/Nov/23

	$2 / (1 / 12 + 1 / 15 + 1 / 20) = 10 m i n u t e s$
	Commented by hardmath last updated on 06/Nov/23

	$thank you so much my dear professor$
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