Question

Pipe $A$ alone can fill one tank in $6$ hours more than it takes pipe $B$ alone to fill one tank. Together, both pipes can fill one tank in $4$ hrs. How long will it take pipe $A$ alone to fill one tank?

• A. $12$ hrs
• B. $10$ hrs
• C. $8$ hrs
• D. None of these

Answer 1

Answer: (A)

$12$ hrs

Let the pipe can fill the tank be x.
Pipe A alone can fill one tank = $\frac{1}{x+6}$
Pipe B alone can fill another tank = $\frac{1}{x}$
Together, both pipes can fill one tank = $\frac{1}{x+6}+\frac{1}{x}=\frac{1}{4}$
$\frac{2x+6}{x^2+6x}=\frac{1}{4}$
$8x+24=x^2+6x$
$x^2-2x-24$
Using $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ to find the roots of the equation
$\Rightarrow x=\frac{2\pm \sqrt{(-2{)}^2-4\times 1\times (-24)}}{2\times 1}$
$\Rightarrow x=\frac{2\pm \sqrt{100}}{2}$
$\Rightarrow x=\frac{2\pm 10}{2}$
$x=6$, $x=-4$
x cannot be negative.
Pipe A alone to fill one tank = 6 + 6 = 12 hours.