On Monday, Hank drove to work at an average speed of $70 \mathrm{~km} / \mathrm{h}$ and arrived 1 minute late. On Tuesday, he left at the same time and took the same route. This time he drove at an average speed of $75 \mathrm{~km} / \mathrm{h}$ and arrived 1 minute early. How long is his route to work?
(A) $30 \mathrm{~km}$
(B) $35 \mathrm{~km}$
(C) $45 \mathrm{~km}$
(D) $50 \mathrm{~km}$
(E) $60 \mathrm{~km}$

## Part C: Each correct answer is worth 8.
Let the length of his route be $d \mathrm{~km}$.

Since he arrives 1 minute early when travelling at $75 \mathrm{~km} / \mathrm{h}$ and 1 minute late when travelling at $70 \mathrm{~km} / \mathrm{h}$, then the difference between these times is 2 minutes, or $\frac{1}{30}$ of an hour.

The time that his trip takes while travelling at $75 \mathrm{~km} / \mathrm{h}$ is $\frac{d}{75}$ hours, and at $70 \mathrm{~km} / \mathrm{h}$ is $\frac{d}{70}$ hours. Therefore,

$$
\begin{aligned}
\frac{d}{70}-\frac{d}{75} & =\frac{1}{30} \\
75 d-70 d & =\frac{75(70)}{30} \\
5 d & =25(7) \\
d & =35
\end{aligned}
$$

Therefore, the route is $35 \mathrm{~km}$ long.

ANswer: (B)