Question

Pipe $A$ can fill a tank in $4$ hrs. If pipe $B$ works alone, it takes $3$ hrs longer to fill the tank than if both pipes work together. How long will it take for pipe $B$ to fill the tank if it works alone?

• A. $5.275$ hrs
• B. $6.275$ hrs
• C. $4.275$ hrs
• D. None of these

Answer 1

The correct option is A $5.275$ hrs

Let the pipe to fill the tank be x.

Pipe A can fill the tank = $\frac{1}{x}$

Pipe B can fill the tank = $\frac{1}{x+3}$

Both pipes working together = $\frac{1}{x}-\frac{1}{x+3}=\frac{1}{4}$

$\frac{3}{x^2+3x}=\frac{1}{4}$

$12=x^2+3x$

$x^2+3x-12=0$

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\Rightarrow \frac{-3\pm \sqrt{(-3{)}^2-4\times 1\times (-12)}}{2\times 1}$

$\Rightarrow \frac{-3\pm \sqrt{57}}{2}$

$\Rightarrow \frac{-3\pm 7.549}{2}$

x = 2.275, x = -5.275

x cannot be negative.

Pipe B to fill the tank = 2.275 + 3 = 5.275 hours.