## Task 2 - 230712

A car is driving on a highway at a constant speed of $80 \frac{\mathrm{km}}{\mathrm{h}}$. A second car is $2 \mathrm{~km}$ behind the first and is driving in the same direction at a constant speed of $85 \frac{\mathrm{km}}{\mathrm{h}}$.

a) How many minutes does the second car need to catch up with the first?

b) How many kilometers does the second car travel until it catches up with the first?
a) Since the speed of the second truck is $5 \frac{\mathrm{km}}{\mathrm{h}}$ higher than that of the first truck, the second truck covers $5 \mathrm{~km}$ more per hour than the first. In $\frac{1}{5}$ h, i.e., 12 minutes, it gets $1 \mathrm{~km}$ closer to the first truck, so it catches up with the first truck in $2 \cdot 12$ minutes $=$ 24 minutes.

b) In this time, it has covered a distance of $85 \cdot \frac{2}{5} \mathrm{~km}=34 \mathrm{~km}$.