13.105. On one of the tram lines, trams of a new design have started to operate. A trip of 20 km now takes 12 minutes less, as the average speed of the new design tram is 5 km/h higher than the average speed of the outdated design tram. How much time does the new design tram take for the trip and what is its average speed?
## Solution.

Let $x$ km/h be the average speed of the new tram model.

Then the time it takes for the trip is $-\frac{20}{x}$ hours. According to the problem, $\frac{20}{x}=\frac{20}{x-5}-\frac{1}{5}$, from which $x=25$ km/h, and the time $-\frac{20}{25}=\frac{4}{5}$ hours $=48$ minutes.

Answer: 48 min, 25 km/h.