Question

Flying against the wind, an airplane travels 2220 kilometers in 3 hours. Flying with the wind, the same plane travels 10,620 kilometers in 9 hours. What is the rate of the plane still in the air and what is the rate of the wind?

Answer 1

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