Answer:the rate of the plane in still air is 830 km/h
the rate of the wind is 160 km/h
Step-by-step explanation:
Let x represent the speed of the plane in still air.
Let y represent the speed of the wind.
Flying against the wind, an airplane travels 3350 kilometers in 5 hours. It means that the total speed of the airplane would be x - y
Distance = speed × time
Therefore
3350 = 5(x - y)
3350 = 5x - 5y - - - - - - - - - - - - 1
Flying with the wind the same plane travels 7920 in 8 hours. It means that the total speed of the airplane would be x + y
Therefore
3350 = 8(x + y)
7920 = 8x + 8y - - - - - - - - - - - - 2
Multiplying equation 1 by 8 and equation 2 by 5, it becomes
26800 = 40x - 40y
39600 = 40x + 40y
Adding both equations, it becomes
66400 = 80x
x = 66400/80
x = 830
Substituting x = 830 into equation 1, it becomes
3350 = 5 × 830 - 5y
3350 = 4150 - 5y
5y = 4150 - 3350 = 800
y = 800/5 = 160
