13.106. The plane must fly 2900 km. Having flown 1700 km, it made an emergency landing for 1 hour 30 minutes, after which it flew at a speed 50 km/h less than before. Find the original speed of the plane, given that it arrived at its destination 5 hours after takeoff.
## Solution.

Let $x$ km/h be the original speed of the airplane. Before landing, it was in the air for $\frac{1700}{x}$ hours, and after landing, it was in the air for $\frac{1200}{x-50}$ hours. According to the condition, $\frac{1700}{x} + 1.5 + \frac{1200}{x-50} = 5$, from which we find $x = 850$ km/h.

Answer: 850 km/h.