Question

An airplane travels 2416 kilometers against the wind in 4 hours and 2896 kilometers with the wind in the same amount of time. What's the rate of the plane in still air and what's the rate of the wind?

Answer 1

Answer: the rate of the plane in still air is 664 km/h and the rate of the wind is 60 km/h

Step-by-step explanation:

Let x represent the rate of the plane in calm air.

Let y represent the rate of the wind.

An airplane travels 2416 kilometers against the wind in 4 hours. This means that the total speed with which the plane flew is (x - y) mph.

Distance = speed × time

Distance travelled by the plane while flying against the wind is

2416 = 4(x - y)

Dividing both sides of the equation by 4, it becomes

604 = x + y- - - - - - - - - - - 1

It flew 2896 kilometers with the wind in the same amount of time.. This means that the total speed with which the plane flew with the wind is (x + y) mph.

Distance travelled by the plane while flying with the wind is

2896 = 4(x + y)

Dividing both sides of the equation by 2, it becomes

724 = x + y- - - - - - - - - - - 2

Adding equation 1 to equation 2, it becomes

1328 = 2x

x = 1328/2

x = 664

Substituting x = 664 into equation 2, it becomes

724 = 664 + y

y = 724 - 664

y = 60