Flying against the wind, an airplane travels kilometers in hours. Flying with the wind, the same plane travels kilometers in hours. What is the rate of the plane in still air and what is the rate of the wind

x = 800 km/h

y = 200 km/h

the rate of the plane in still air is 800 km/h

and the rate of the wind is 200 km/h

Completed question;

Flying against the wind, an airplane travels 4200 km in 7 hours. Flying with the wind, the same plane travels 4000 km in 4 hours. What is the rate of the plane in still air and what is the rate of the wind?

Step-by-step explanation:

Let x and y represent the rate of the plane and wind respectively;

When flying against the wind, the relative speed is;

Va = x-y ... 1

When flying with the wind, the relative speed is;

Vb = x+y ... 2

Distance = speed * time

Speed = distance/time

v = d/t

Given;

Flying against the wind, an airplane travels 4200 km in 7 hours. Flying with the wind, the same plane travels 4000 km in 4 hours

When flying against wind;

distance da = 4200 km

time ta = 7 hours

Va = da/ta = 4200/7

Va = 600 km/h

Substituting equation 1

x-y = 600 ... 3

When flying with wind;

distance db = 4000 km

Time tb = 4 hours

Vb = db/tb = 4000/4

Vb = 1000 km/h

Substituting equation 2;

x + y = 1000 ... 4

Adding equation 3 and 4;

x-y + (x+y) = 600 + 1000

2x = 1600

x = 1600/2

x = 800 km/h

Substituting x = 800 into equation 3;

800 - y = 600

y = 800 - 600

y = 200 km/h

Therefore, the rate of the plane in still air is 800 km/h

and the rate of the wind is 200 km/h.