13.031. A group of students went on a hike through the Moscow region during their vacation. The first 30 km they walked, $20 \%$ of the remaining part of the route they traveled by raft along the river, and then they walked again, covering a distance 1.5 times greater than the distance they traveled by raft. The remaining part of the journey was covered in 1 hour 30 minutes by hitching a ride on a passing truck, which was traveling at a speed of 40 km/h. What is the total length of the route?
## Solution.

Let $x$ km be the total length of the route. Then the students floated on a raft for $(x-30) \cdot 0.2$ km, and then walked another $1.5(x-30) \cdot 0.2$ km. According to the problem, $30+(x-30) \cdot 0.2+1.5(x-30) \cdot 0.2+40 \cdot 1.5=x$, from which $x=150$ km.

Answer: 150 km.