Problem 9.2. Anton, Vasya, Sasha, and Dima were driving from city A to city B, each taking turns at the wheel. The car traveled the entire distance at a constant speed.

Anton drove for half the time Vasya did, and Sasha drove as much as Anton and Dima combined. Dima was behind the wheel for only one-tenth of the journey. What fraction of the journey was Vasya driving? Write your answer as a decimal.
Answer: 0.4.

Solution. Let Anton drive $a$ kilometers, Vasya - $b$ kilometers, Sasha - $c$ kilometers, and Dima - $d$ kilometers.

Anton drove the car twice as little as Vasya. Therefore, $2a = b$.

Sasha drove the car as much as Anton and Dima combined. Therefore, $c = a + d$. Writing the chain of equalities $2a + 2c = 2a + c + c = b + c + (a + d)$, we get

$$
a + c = \frac{a + b + c + d}{2}
$$

Therefore, Anton and Sasha together drove half of the journey, so Vasya and Dima together drove the other half of the journey. Since Dima drove 0.1 part of the journey, Vasya drove the car 0.4 part of the journey.

Another solution. Let the fraction of the journey during which Anton was driving be $x$. Then the fraction for Vasya is $2x$, for Dima - 0.1, and for Sasha - $0.1 + x$. Summing all the fractions, we get $4x + 0.2$, which should equal 1. From this, $x = 0.2$; and the answer is $2x = 0.4$.