1. Andrei was driving to the airport of a neighboring city. After an hour of driving at a speed of 60 km/h, he realized that if he did not change his speed, he would be 20 minutes late. Then he sharply increased his speed, as a result of which he covered the remaining part of the journey at an average speed of 90 km/h and arrived at the airport 20 minutes earlier than originally planned. What is the distance from Andrei's home to the airport?
Answer: 180 km.

Solution. Let the distance from Andrey's house to the airport be $s$ km, and the time he intended to spend on the road be $1+t$ hours. Then

$$
s=60+60\left(t+\frac{1}{3}\right)=60+90\left(t-\frac{1}{3}\right)
$$

From this,

$$
60 t+20=90 t-30, \quad t=\frac{5}{3}, \quad s=180
$$

Evaluation. Full score for the solution is 12 points.