13.109. Two cyclists set off simultaneously towards each other from two places, the distance between which is 270 km. The second cyclist travels 1.5 km less per hour than the first, and meets him after as many hours as the first cyclist travels in kilometers per hour. Determine the speed of each cyclist.
## Solution.

Let $x$ km/h be the speed of the first cyclist, and $x-1.5$ km/h be the speed of the second cyclist. Before they meet, the first cyclist traveled $x \cdot x$ km, and the second cyclist traveled $x(x-1.5)$ km. According to the problem, $x^{2}+x(x-1.5)=270$, from which $x=12$ km/h; $12-1.5=10.5$ km/h.

Answer: 12 and 10.5 km/h.