7.1. Before a running competition, Petya planned to run the entire distance at a constant speed $V$. However, upon learning the results of his competitors, Petya decided to increase his planned speed by $25 \%$. With this increased speed, he ran half the distance, but then got tired, so he ran the second half of the distance at a speed $20 \%$ lower than the speed $V$. Did Petya's time turn out to be more or less than the planned time?
Answer: more than planned. Solution. Let $a$ be the length of the distance. Then the planned time is $\frac{a}{V}$, and the actual time is $\frac{a}{2 \cdot 1.25 V}+\frac{a}{2 \cdot 0.8 V}=\frac{a}{V} \cdot \frac{41}{40}>\frac{a}{V}$.