Question

It takes $6$ hours for pump A, used alone, to fill a tank of water. Pump B used alone takes $8$ hours to fill the same tank. We want to use three pumps A,B and C to fill the tank in $2$ hours. What should be the rate of pump C? How ling would it take pump C, used alone, to fill the tank?

Answer 1

Let Volume of Tank be $V$

pipe $A$ can fill the tank $\frac{V}{6}$ in 1 Hour

pipe $B$ can fill the tank $\frac{V}{8}$ in 1 Hour

Let us assume that $C$ can fill the tank $\frac{V}{C}$ in 1 Hour

and we need to fill the tank $\frac{V}{2}$ in 1 Hour as we have to fill the complete tank in $2$ Hrs

$\Rightarrow \frac{V}{6}+\frac{V}{8}+\frac{V}{C}=\frac{V}{2}$

$\Rightarrow \frac{1}{6}+\frac{1}{8}+\frac{1}{C}=\frac{1}{2}$

solving we get $C=\frac{24}{5}hrs$

Rate of Pumping is $\frac{V}{\frac{24}{5}}$

Time to fill the Tank when $C$ is used alone$=\frac{24}{5}=4.8hrs$