3. Postman Pechkin is riding a bicycle along a highway. He noticed that every 4.5 kilometers, a suburban bus overtakes him, and every 9 minutes, a suburban bus passes him in the opposite direction. The interval of bus movement in both directions is 12 minutes. At what speed is Pechkin riding?
Answer: 15 km/h

Solution: Let x (km/h) and y (km/h) be the speeds of the cyclist and the bus, respectively. Since the interval between bus movements is 12 minutes (1/5 hour), the distance between two consecutive buses is y/5 km. Therefore, at the moment the cyclist meets a bus, the distance between the cyclist and the next oncoming bus is y/5 km. Since their meeting will occur in 9 minutes (3/20 hour), and the closing speed is (x+y), we have $3(x+y)/20=y/5$. The time between two consecutive overtakes is 4.5/x, on the other hand, it is equal to $1/5 + 4.5/y$. Thus, we have the system of equations $3(x+y)=4y$ and $4.5/x=1/5+4.5/y$, from which $x=15$ km/h.

Grading criteria: Correct solution - 7 points, the solution process is correct but the answer is wrong due to an arithmetic error - **5** points, the system is set up but the subsequent solution is incomplete or incorrect - **3** points, in all other cases - 0 points.