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 separately, find the time in which each pipe would fill the tank separately.

Answer 1

Let the time taken by the one tap to fill the tank be x minutes.

then, other pipe takes $(x+5)$ minutes to fill the tank.

According to the question,

$\frac{1}{x}+\frac{1}{x+5}=\frac{1}{100/9}$

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

$\Rightarrow 100(5+2x)=9x(x+5)$

$\Rightarrow 500+200x=9x^2+45x$

$\Rightarrow 9x^2+45x-200x-500=0$

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

$\Rightarrow 9x^2-180x+25x-500=0$

$\Rightarrow 9x(x-20)+25(x-20)=0$

$\Rightarrow (9x+25)(x-20)=0$

$x=20$ or $-\frac{25}{9}$ (Neglect negative val;uie of $x$)

$\therefore x=20$

$\therefore$ Time in which each pipe would fill the tank separately are 20 mins and 25 mins respectively.