## Task 3 - 090723

A tourist was on the road for exactly the same amount of time on three consecutive days.

On the first day, he walked with an average speed of $6 \mathrm{~km} / \mathrm{h}$. On the second day, he used a moped with an average speed of $30 \mathrm{~km} / \mathrm{h}$. On the third day, he used a car with an average speed of $60 \mathrm{~km} / \mathrm{h}$. The total distance traveled over the three days was $520 \mathrm{~km}$.

Determine the time he was on the road each of the three days, and the number of kilometers traveled on the first, second, and third days!
The distances covered on individual days are proportional to the respective average speeds. The distance covered on the second and third day is thus 5 and 10 times the distance covered on the first day, respectively.

Since $1+5+10=16$, the total distance, which is $520 \mathrm{~km}$ according to the problem statement, is 16 times the distance covered on the first day.

This is only possible if the distance covered on the first day is $520 \mathrm{~km} \div 16 = 32.5 \mathrm{~km}$, and consequently, the distances covered on the second and third days are $5 \cdot 32.5 \mathrm{~km} = 162.5 \mathrm{~km}$ and $10 \cdot 32.5 \mathrm{~km} = 325 \mathrm{~km}$, respectively.

From this, it follows that $\frac{32.5}{6} = \frac{65}{12} = 5 \frac{25}{60}$, which gives the time spent on the first day (and, according to the problem statement, on each of the three days) as $\frac{65}{12} \mathrm{~h} (=5 \mathrm{~h} 25 \mathrm{~min})$.