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
