1. Viktor was driving to the airport of a neighboring city. After half an hour of driving at a speed of 60 km/h, he realized that if he did not change his speed, he would be 15 minutes late. Then he increased his speed, as a result of which he covered the remaining part of the journey at an average speed of 80 km/h and arrived at the airport 15 minutes earlier than originally planned. What is the distance from Viktor's home to the airport?
Answer: 150 km.

Solution. Let the distance from Viktor's house to the airport be $s$ km, and the time he intended to spend on the road $\frac{1}{2}+t$ hours. Then

$$
s=30+60\left(t+\frac{1}{4}\right)=30+80\left(t-\frac{1}{4}\right)
$$

From this,

$$
60 t+15=80 t-20, \quad t=\frac{7}{4}, \quad s=150
$$

Evaluation. Full solution: 12 points.