13.196. Two hours after leaving the factory, the driver looked at the speedometer and noticed that he had only traveled 112 km. He mentally calculated that if he continued at the same speed, he would be 30 minutes late in delivering the cargo to the station. Therefore, the driver increased his speed and arrived at the station even 30 minutes early. Determine the initial and subsequent speeds of the car, if the distance from the factory to the station according to the speedometer is 280 km.
Solution.

The initial speed of the car is $\frac{112}{2}=56$ km/h. The driver was on the road for a total of $\frac{280}{56}-1=4$ hours. Let the driver increase the speed by $x$ km/h. With this speed, he drove for 2 hours and covered $280-112=168$ km. Therefore, $2(56+x)=168$, from which the new speed of the car is $84 \mathrm{km} / \mathrm{h}$.

Answer: 56 and 84 km/h.