Flying against the wind, an airplane travels 5100 kilometers in 6 hours. flying with the wind, the same plane travels 3870 kilometers in 3 hours. what is the rate of the plane in still air and what is the rate of the wind?

The rate of the plane in still air is 1070 km/h and what is the rate of the wind is 220 Km/h

Step-by-step explanation:

Relative Speeds

If an object moves at a speed with respect to another object at a speed , the relative speeds between them can be or depending if they are collaborative or one against the other.

The speed of an object who travels a distance x in a time t is

We know that an airplane travels 5100 kilometers in 6 hours when flying against the wind, and travels 3870 kilometers in 3 hours when flying with the wind. Let's call and the speeds of the plane in still air and the wind, respectively. The first travel is performed by the plane with a wind whose speed subtracts from its own, so the relative speed is

The second travel is performed with the wind pushing in the same direction, so

Adding both equations, we have

Simplifying and solving

Replacing into the second equation

The rate of the plane in still air is 1070 km/h and what is the rate of the wind is 220 Km/h