It takes Sharon one hour to drive the $59 \mathrm{~km}$ from her home to her office. Her drive includes 20 minutes on a highway and 40 minutes on city roads. If her average speed when she is on city roads is $45 \mathrm{~km} / \mathrm{h}$, the average speed, in $\mathrm{km} / \mathrm{h}$, at which she drives on the highway is
(A) 42
(B) 59
(C) 87
(D) 90
(E) 100
In her 40 minutes (or $\frac{2}{3}$ of an hour) on city roads driving at an average speed of $45 \mathrm{~km} / \mathrm{h}$, Sharon drives $\left(\frac{2}{3} \mathrm{~h}\right) \times(45 \mathrm{~km} / \mathrm{h})=30 \mathrm{~km}$. So the distance that she drives on the highway must be $59 \mathrm{~km}-30 \mathrm{~km}=29 \mathrm{~km}$. Since she drives this distance in 20 minutes (or $\frac{1}{3}$ of an hour), then her average speed on the highway is $\frac{29 \mathrm{~km}}{\frac{1}{3} \mathrm{~h}}=(29 \times 3) \mathrm{km} / \mathrm{h}=87 \mathrm{~km} / \mathrm{h}$.

Answer: (C)