9.3. The road from Kimovsk to Moscow consists of three sections: Kimovsk - Novomoskovsk (35 km), Novomoskovsk - Tula (60 km), and Tula - Moscow (200 km). A bus, whose speed nowhere exceeded 60 km/h, traveled from 

Kimovsk to Tula in 2 hours, and from Novomoskovsk to Moscow in 5 hours. How long could the bus have been on the road?
Answer: From $5 \frac{7}{12}$ to 6 hours.

Solution. The total travel time is obtained by subtracting from the sum of $2+5$ the time spent on the segment Novomoskovsk - Tula. According to the condition, the bus spent no less than an hour on this segment (60 km). On the other hand, the journey from Kimovsk to Novomoskovsk took no less than $\frac{35}{60}=\frac{7}{12}$ hours, so the time left for the journey from Novomoskovsk to Tula is no more than $2-\frac{7}{12}=1 \frac{5}{12}$. Therefore, the total travel time is no more than $7-1=6$ hours and no less than $7-1 \frac{5}{12}=5 \frac{7}{12}$ hours.

We will show that any time in this interval is possible. To travel the entire route in $6-t\left(0 \leq t \leq \frac{5}{12}\right)$, the bus needs to travel the segment Kimovsk - Novomoskovsk in $1-t \geq \frac{7}{12}$, the segment Novomoskovsk - Tula in $1+t$, and the segment Tula - Moscow in $4-t \geq 3 \frac{7}{12}$, which fits within the speed limit, as $\frac{200}{60}=3 \frac{1}{3}<3 \frac{7}{12}$.

Comment. Answer 6 and (or) $5 \frac{7}{12}$ - 1 point each, if the correct answer is obtained but it is not proven that any time in the interval is possible - 5 points.