I'm having trouble understanding how to approach Problem 130 in I.M. Gelfand's book. Preceding this problem he shows us the definition of the harmonic mean:
$\frac{1}{\quad\frac{\frac{1}{a} + \frac{1}{b}}{2}\quad} = \frac{2}{\frac{1}{a}+\frac{1}{b}}$
He then states problem 130, which is:
A swimming pool is divided into two equal sections. Each section has its own water supply pipe. To fill one section (using its pipe) you need $a$ hours. To fill the other section you need $b$ hours. How many hours would you need if you turn on both pipes and remove the wall dividing the pool into sections.
So I'm having trouble understanding how to apply the harmonic mean to this problem. Any hints or guidance would really be appreciated.