jmc

Let $d$ denote the number of miles in the distance from $A$ to $B$ and let $r$ denote the speed of the car (in miles per hour) on the return trip. It takes $d/60$ hours to travel from $A$ to $B$ and $d/r$ hours to travel from $B$ to $A$. Round trip, $2d$ miles are covered in $d/60+d/r$ hours for an average speed of $$\frac{2d}{\frac{d}{60}+\frac{d}{r}}\cdot \frac{\frac{60}{d}}{\frac{60}{d}}=\frac{120}{1+\frac{60}{r}}$$ Setting this expression equal to $45$, we find $r=\boxed{36}$.