Originally Posted by

**algebraic topology** I’ve just worked through the problem, and I think it should be $\displaystyle 3\frac{1}{\color{red}13}$ minutes, not $\displaystyle 3\frac{1}{3}$ minutes.

No, the equation is

$\displaystyle \frac{1}{x}+\frac{1}{x-3}\ =\ \frac{1}{3\frac{1}{13}}$

where $\displaystyle \frac{1}{x}$ is the fraction of the cistern filled in 1 minute by one of the pipes and $\displaystyle \frac{1}{x-3}$ in 1 minute by the other; $\displaystyle \frac{1}{3\frac{1}{13}}$ is the fraction of the cistern filled in 1 minute by both pipes together.