Two pipes A and B together can fill a cistern in 4 hours. If they had been opened separately, pipe B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

Let pipe A alone fill the cistern in x hours.

∴ Time taken by pipe B = (x + 6) hours

According to the question, $\frac{1}{x}+\frac{1}{x+6}=\frac{1}{4}$

$\Rightarrow \frac{x+6+x}{x(x+6)}=\frac{1}{4}$

⇒ 8x + 24 = x² + 6

⇒ x² – 2x – 24 = 0

⇒ x² – 6x + 4x – 24 = 0

⇒ x(x – 6) + 4(x – 6) = 0

⇒ (x + 4) (x – 6) = 0 ⇒ x = 6

because x ≠ –4