Petr and Honza went swimming. The distances they swam were in the ratio $4: 5$, with Honza swimming more. The next day, they went again, this time Petr swam 200 meters less and Honza swam 100 meters more than the previous day, and the ratio of distances was $5: 8$. How many meters did Honza and Petr swim on the first day?

(B. Š'astná)
The ratio of the distances that Petr and Honza swam on the first day is $4: 5$. This means that Petr swam $4 x$ meters and Honza $5 x$ meters. The next day, Petr swam $(4 x-200)$ meters, and Honza $(5 x+100)$ meters. If these distances are in the ratio $5: 8$, then:

$$
\begin{aligned}
8 \cdot(4 x-200) & =5 \cdot(5 x+100) \\
x & =300 \mathrm{~m} .
\end{aligned}
$$

Therefore: Petr swam $4 \cdot 300=1200 \mathrm{~m}$ on the first day, and Honza $5 \cdot 300=1500 \mathrm{~m}$.