Answer
$t=10$ minutes.
Work Step by Step
In 1 minute,
the faucet fills $\displaystyle \frac{1}{5}$ of the sink's volume,
and the drain drains $\displaystyle \frac{1}{10} $ of the sink's volume.
In $t$ minutes, $\displaystyle \quad\frac{t}{5}-\frac{t}{10}$ of the sink is filled
We want the t (in minutes) when this equals $\displaystyle \frac{1}{1}$ of sink volume.
$\displaystyle \frac{t}{5}-\frac{t}{10}=1\qquad.../\times 10$
$2t-t=10$
$t=10$ minutes.
