Answer
$t=18$ minutes,
which is enough before the parents return.
Work Step by Step
In 1 minute,
I do $\displaystyle \frac{1}{45}$ of the full job,
my sister does $\displaystyle \frac{1}{30}$ of the full job.
In $t$ minutes, we complete $(\displaystyle \frac{t}{45}+\frac{t}{30})$ of the job.
We want t for which $\displaystyle \frac{1}{1}$ of the job is done (the whole job).
$\displaystyle \frac{t}{45}+\frac{t}{30}=1\qquad$
...$\left[\begin{array}{rrr}
45=9\times 5&=\fbox{$5$}\times\fbox{$3$}\times 3\\
30=5\times6&=\fbox{$5$}\times\fbox{$3$}\times 2
\end{array}\right]$,
... LCD=$5\times 3\times 3\times 2=90$
...multiply with 90
$2t+3t=90$
$5t=90$
$t=18$ minutes,
which is enough before the parents return.
