Algebra-Pipe-A-can-fill-a-tank-in-two-hours-and-pipe-B-can-fill-it-in-half-the-time-it-takes-pipe-C-to-empty-it-When-all-3-are-opened-it-takes-1-5-hours-to-fill-the-pool-how-much-time-is-required-fo

Question Number 135420 by liberty last updated on 13/Mar/21

$$Algebra$$Pipe A can fill a tank in two hours and pipe B can fill it in half the time it takes pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool how much time is required for pipe 'C to empty the tank?

Answered by john_santu last updated on 13/Mar/21

$$\left(1\right)pipeA\Rightarrow V_1=\frac{W}{2}$$$$\left(2\right)pipeC\Rightarrow V_2=\frac{W}{a}$$$$\left(3\right)pipeB\Rightarrow V_3=\frac{W}{a/2}$$$$\left(4\right)Whenall3pipeareopened$$$$\Rightarrow \frac{W}{V_1+V_2+V_3}=\frac{3}{2}$$$$\Rightarrow \frac{W}{\frac{W}{2}+\frac{W}{a}+\frac{2W}{a}}=\frac{3}{2}$$$$\Rightarrow \frac{1}{2}+\frac{3}{a}=\frac{2}{3};\frac{3}{a}=\frac{1}{6}$$$$wegeta=18hour$$$$$$

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