Question

Two pipes running together can fill a tank in $11\frac{1}{9}$ minutes. If one pipe takes $5$ minutes more than the other to fill the tank , find the product of the time in which each pipe would fill the tank .

Answer 1

Two pipes together fill tank in $11\frac{1}{9}$ min.

Let the time taken by one pipe to fill them separately be $x$ min.

Time taken by another pipe to fill tank separately is $x+5$ min.

$\Rightarrow \frac{\left(x\right)(x+5)}{x+x+5}=\frac{100}{9}$

$\Rightarrow 9(x^2+5x)=200x+500$

$\Rightarrow 9x^2-155x-500=0$

$x=\frac{155\pm 205}{2\left(9\right)}$

$\Rightarrow x=\frac{360}{2\left(9\right)}$

$\Rightarrow x=20$ - Equation 1

$\Rightarrow x+5=25$ -Equation 2

Product of times taken by them both separately=$\left(x\right)(x+5)=500$