7.1. A cyclist was initially traveling at a speed of 20 (km/h). After covering one-third of the distance, he glanced at his watch and decided to increase his speed by 20%. He continued the rest of the journey at the new speed. What was the cyclist's average speed?
Answer: 22.5 km/h. Solution. Let $a$ be the distance, $v=20($ km/h) be the initial speed. Then the new speed is $1.2 v$. The entire journey will take $\frac{a}{3 v}+\frac{2 a}{3 \cdot 1.2 v}=\frac{8}{9} \frac{a}{v}$ (hours). Thus, the average speed is $a: \frac{8}{9} \frac{a}{v}=\frac{9}{8} v=22.5$ (km/h).