13.285. On a 10 km stretch of highway, devoid of intersections, the bus stops only for passengers to get on and off. It makes a total of 6 intermediate stops, spending 1 minute at each, and always moves at the same speed. If the bus were to travel without stopping, it would cover the same distance at a speed exceeding the average speed of its movement with stops by 5 km/h. How many minutes is the bus in motion on this stretch of highway?
Solution.

Let $t$ min be the time the bus is in motion on the segment. Then its average speed without stops is $-\frac{10}{t}$, and with stops, it is $-\frac{10}{t+\frac{1}{60} \cdot 6}$.

According to the condition, $\frac{10}{t+0.1}+5=\frac{10}{t}$, from which $t=24$ (min).

Answer: 24 min.