## Task 6 - 190836

A taxi driver was supposed to pick up a guest from the train station at 15:00. With an average speed of $50 \frac{\mathrm{km}}{\mathrm{h}}$, he would have arrived on time. Due to unfavorable traffic conditions, he could only drive at an average speed of $30 \frac{\mathrm{km}}{\mathrm{h}}$ and therefore arrived at the station at 15:10.

a) Calculate the length of the distance the driver covered to the station!

b) Calculate the time the driver needed to reach the station!
a) At a speed of $30 \frac{\mathrm{km}}{\mathrm{h}}$, the taxi driver covered a distance of $30 \cdot \frac{1}{6} \mathrm{~km}=5$ $\mathrm{km}$ in 10 minutes. For this distance, he would have needed a time of $\frac{5}{50} \mathrm{~h}=\frac{1}{10} \mathrm{~h}=6$ min at a speed of $50 \frac{\mathrm{km}}{\mathrm{h}}$.

For every $5 \mathrm{~km}$, the taxi driver therefore needed $4 \mathrm{~min}$ more than he would have needed at a speed of $50 \frac{\mathrm{km}}{\mathrm{h}}$. Since he was exactly $10 \mathrm{~min}$ late, he had covered a total distance of $\frac{5}{4} \cdot 10=12.5$ km.

b) For the distance of $12.5 \mathrm{~km}$, a time of $\frac{12.5}{30} \mathrm{~h}=\frac{5}{12} \mathrm{~h}=25$ min is required at a speed of $30 \frac{\mathrm{km}}{\mathrm{h}}$.

Solutions of the III. Round 1979 taken from [5]

### 5.22 XX. Olympiad 1980

### 5.22.1 I. Round 1980, Class 8