13.089. A train traveled a certain distance at a speed of 120 km/h. After that, it traveled a distance 75 km longer at a speed of 150 km/h, and the remaining distance, 135 km shorter than the distance traveled, at a speed of 96 km/h. How long is the entire journey if the average speed of the train turned out to be 120 km/h?
Solution.

| Section | Distance | Speed | Time |
| :---: | :---: | :---: | :---: |
| First | $x \mathrm{km}$ | $120 \mathrm{km} / \mathrm{h}$ | $\frac{x}{120} \mathrm{h}$ |
| Second | $75+x \mathrm{km}$ | $150 \mathrm{km} / \mathrm{h}$ | $\frac{75+x}{150} \mathrm{h}$ |
| Third |  |  |  |

The entire distance is $x+75+x+2x-60=4x+15$, the total time is $\frac{x}{120}+\frac{75+x}{150}+\frac{2x-60}{96}=\frac{43x-150}{1200}$. The average speed of the train: $\frac{4x+15}{\frac{43x-150}{1200}}=120$.

From this, $x=100$ km. The entire distance will be: $4 \cdot 100+15=415$ km.

Answer: 415 km.