Task 4. (20 points) To get from the first to the second building of the university, Sasha took a car-sharing vehicle, while Valya rented a scooter. Sasha and Valya set off from the first building to the second at the same time, and at the same time, teacher Sergei Vladimirovich set off from the second building to the first in a car. The cars met after 4 minutes, and the scooter and the teacher's car met 1 km from the main building. Find the speeds of the cars and the scooter, if the scooter takes 1.4 hours longer to cover a distance of 18 km compared to the car-sharing vehicle, and its speed is 6 times less than the speed of Sergei Vladimirovich's car. In your answer, indicate the speeds in $\frac{\kappa M}{\psi}$ in ascending order.
# Solution.

Since the speeds of the scooter and the teacher's car differ by 6 times, the teacher's car will travel 6 times more in the same amount of time. Therefore, the distance between the buildings is $1+6=7$ km.

Let $x$ be the speed of the scooter, $t$ be the time the car-sharing service spends traveling 20 km, $s$ be the distance the car-sharing car travels before meeting the teacher's car, and $v$ be the speed of the car-sharing service.

Solving the system:

![](https://cdn.mathpix.com/cropped/2024_05_06_b2236406d6db6e8875c1g-08.jpg?height=317&width=650&top_left_y=1932&top_left_x=406)

Answer. $10,45,60$.