Answer
$t=20$ minutes,
which leaves enough time to make it to class.
Work Step by Step
In 1 minute,
I do $\displaystyle \frac{1}{45}$ of the full job,
my brother does $\displaystyle \frac{1}{36}$ of the full job.
In $t$ minutes, we complete $(\displaystyle \frac{t}{45}+\frac{t}{36})$ of the job.
We want t for which $\displaystyle \frac{1}{1}$ of the job is done (the whole job).
To make it to campus, t should be less than 30 minutes.
$\displaystyle \frac{t}{45}+\frac{t}{36}=1\qquad$
...$\left[\begin{array}{l}
45=9\times 5=5\times\fbox{$3$}\times\fbox{$3$}\\
36=6\times 6=\fbox{$3$}\times\fbox{$3$}\times 2\times 2
\end{array}\right]$,
... LCD=$5\times 3\times 3\times 2\times 2=180$
... multiply with $180$
$4t+5t=180$
$9t=180$
$t=20$ minutes,
which leaves enough time to make it to class.
