Driving between two towns at $110 \mathrm{~km} / \mathrm{h}$ instead of $100 \mathrm{~km} / \mathrm{h}$ saves 9 minutes. The distance in kilometres between the two towns is
(A) 210
(B) 99
(C) 165
(D) 9900
(E) 150

## Part C: Each question is worth 8 credits.
Driving between two towns at $110 \mathrm{~km} / \mathrm{h}$ instead of $100 \mathrm{~km} / \mathrm{h}$ saves 9 minutes. The distance in kilometres between the two towns is
(A) 210
(B) 99
(C) 165
(D) 9900
(E) 150

## Solution

Let $x$ represent the distance, in kilometres, between the two towns. Driving at $100 \mathrm{~km} / \mathrm{h}$, it takes $\frac{x}{100}$ hours to travel between the towns. Driving at $110 \mathrm{~km} / \mathrm{h}$, it takes $\frac{x}{110}$ hours. We know that these two times differ by 9 minutes, or $\frac{9}{60}$ hours.

Thus, $\frac{x}{110}+\frac{9}{60}=\frac{x}{100}$

$$
\begin{aligned}
\frac{x}{11}+\frac{3}{2} & =\frac{x}{10} \\
\frac{3}{2} & =\frac{11 x}{110}-\frac{10 x}{110} \\
\frac{3}{2} & =\frac{x}{110} \\
165 & =x
\end{aligned}
$$

The two towns are $165 \mathrm{~km}$ apart.

ANSWER: (C)

## PART C: