1. One tourist covers a distance of 20 km 2.5 hours faster than the other. If the first tourist reduced their speed by 2 km/h, and the second increased their speed by 50%, they would spend the same amount of time on the same distance. Find the speeds of the tourists.
Solution: Let $\mathrm{x}$ be the speed of the first tourist, and $y$ be the speed of the second tourist. 
\[
\frac{20}{x}+\frac{5}{2}=\frac{20}{y}, \quad x-2=1.5 y, \quad \frac{4}{x}+\frac{1}{2}=\frac{6}{x-2}, \quad x^{2}-6 x-16=0, \quad x=8, \quad y=4
\]

Answer: $8 \mathrm{km} / \mathrm{u}, 4 \mathrm{km} / \mathrm{q}$.