2. The airplane flew the first $385 \mathrm{~km}$ at a speed of $220 \mathrm{~km} / \mathrm{h}$. The remaining part of the journey was flown at a speed of $330 \mathrm{~km} / \mathrm{h}$. The average speed for the entire trip was $250 \mathrm{~km} / \mathrm{h}$. How far did the airplane fly?
Solution. The first part of the journey, the plane flew for $\frac{385}{220}=3.5$ hours. The remaining part of the journey, i.e., $x \text{ km}$, the plane flew for $t$ hours. From this, we get the equations $x=330 t$ and
![](https://cdn.mathpix.com/cropped/2024_06_05_6f06ce47627480a4d953g-3.jpg?height=286&width=452&top_left_y=446&top_left_x=1014)
$385+x=250(3.5+t)$. If we substitute $t=\frac{x}{330}$ from the first equation into the second equation, we get the equation

$$
385+x=250\left(3.5+\frac{x}{330}\right)
$$

whose solution is $x=2021.25 \text{ km}$. Therefore, the plane flew a total of $2406.25 \text{ km}$.