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
$${Let}\:{volume}\:{of}\:{pool}\:{be}\:{a};{speed}\:{of}\:{pipes}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4} \\ $$$${be}\:{w},{x},{y},{z}\:\left({vol}/{min}\right)\Rightarrow{w}+{x}+{y}=\frac{{a}}{\mathrm{12}}…\left({i}\right) \\ $$$${x}+{y}+{z}=\frac{{a}}{\mathrm{15}}…\left({ii}\right);{w}+{z}=\frac{{a}}{\mathrm{20}}…\left({iii}\right); \\ $$$$\left({i}\right)−\left({ii}\right)\Rightarrow{w}−{z}=\frac{{a}}{\mathrm{60}}\Rightarrow\mathrm{2}{w}=\frac{\mathrm{4}{a}}{\mathrm{60}}\Rightarrow{w}=\frac{{a}}{\mathrm{30}} \\ $$$$\Rightarrow{x}+{y}=\frac{{a}}{\mathrm{20}}\Rightarrow{w}+{x}+{y}+{z}=\frac{{a}}{\mathrm{10}} \\ $$$$\Rightarrow{All}\:{pipes}\:{will}\:{fill}\:{in}\:\mathrm{10}\:{minutes} \\ $$
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
$$\mathrm{2}/\left(\mathrm{1}/\mathrm{12}+\mathrm{1}/\mathrm{15}+\mathrm{1}/\mathrm{20}\right)=\mathrm{10}\:{minutes} \\ $$
Commented by hardmath last updated on 06/Nov/23
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much}\:\mathrm{my}\:\mathrm{dear}\:\mathrm{professor} \\ $$