Answer:
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.
