Two pipes together drain a wastewater holding tank in 6 hours. If used alone to empty the tank, one takes 2 hours longer than the other. How long does each take to empty the tank when used alone?
W is the emptying of the tank.
x is the time of the one tube.
x-2h is the time of the other tube.
\(\large W=(\frac{W}{x}+\frac{W}{x-2h})\times 6h\)
\(\large\frac{1}{6h}= \frac{1}{x}+\frac{1}{x-2h}\)
\(\large\frac{1}{6h}=\frac{x-2h+x}{x^2-2hx}\)
\(\large\frac{x^2-2hx}{6h}=2x-2h\)
\(\large x^2-2hx-12hx+12h^2=0\)
\(\large x^2-14hx+12h^2=0\)
\(\large x=7h\pm\sqrt{49h^2-12h^2}=7h\pm6.08276\)
\(x_{a1}=13.0827h=13h \ 4 min \ 58 sec\)
\((x_{a1}-2h)_b=11h \ 4min \ 58sec \)
\(x_{a2}=0.917237h=55min \ 2sec\)
\((x_{a2}-2h)_b=-(1h \ 4min\ 58sec β Flow \ rate)\)
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