Task 4. (20 points) To get from the first to the second building of the university, Sasha took a car-sharing vehicle, while Zhenya rented a scooter. Sasha and Zhenya left the first building for the second at the same time, and at the same time, Professor Vladimir Sergeyevich left the second building for the first in a car. The cars met after 3 minutes, and the scooter and the professor's car met 1 km from the first building. Find the speeds of the cars and the scooter, if the scooter takes 1.25 hours longer to cover a distance of 30 km compared to the car-sharing vehicle, and its speed is 4 times less than the speed of Professor Vladimir Sergeyevich's car. In your answer, indicate the speeds in $\frac{\kappa M}{4}$ in ascending order.
# Solution.

Since the speeds of the scooter and the teacher's car differ by a factor of 4, the teacher's car will travel 4 times the distance in the same amount of time. Therefore, the distance between the buildings is $1+4=5$ km.

Let $x$ be the speed of the scooter, $t$ be the time the car-sharing service spends traveling 30 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:

$$
\left\{\begin{array} { r l } 
{ \frac { 3 0 } { x } } & { = t + 1 . 2 5 } \\
{ \frac { 5 - s } { 4 x } } & { = \frac { s } { v } = 0 . 0 5 , } \\
{ t v } & { = 3 0 }
\end{array} \quad \text { we get } \left\{\begin{array}{c}
x=15 \\
t=0.6 \\
s=2 \\
v=40
\end{array}\right.\right.
$$

Answer. 15, 40, 60.