Answer:
Rate of the plane in air = 960 kilometers per hour
Rate of the wind = 220 kilometers per hour
Explanations:
Note:
Rate = Distance traveled/ time
Let a represent the rate of the airplane in air
Let b represent the rate of the wind
When the airplane travels against the wind, the rate becomes a - b
When the airplane travels with the wind, the rate becomes a + b
Let the distance travelled by the airplane against the wind be d₁
d₁ = 2220 km
Let the time spent by the airplane in travelling against the wind be t₁
t₁ = 3 hours
Rate against the wind = (Distance traveled against the wind) / time taken
a - b = d₁ / t₁
a - b = 2220/3
a - b = 740...............(1)
Let the distance travelled by the airplane with the wind be d₂
d₂ = 10620 km
Let the time spent by the airplane in travelling with the wind be t₂
t₂ = 9 hours
Rate with the wind = (Distance traveled with the wind) / time taken
a + b = d₂ / t₂
a + b = 10620/9
a + b = 1180...............(2)
Solve equations (1) and (2) simulataneously to get a and b
Add equations (1) and (2) together:
2a = 1920
a = 1920/2
a = 960
Rate of the plane in air = 960 kilometers per hour
Subtract equation (1) from equation(2)
2b = 440
b = 440/2
b = 220
The rate of the wind = 220 kilometers per hour