Answer:
The rate of plane in still air is 1020 kilometers per hour and rate of wind is 180 kilometers per hour.
Step-by-step explanation:
Given that:
An airplane travels 5040 kilometers in 6 hours against the wind
An airplane travels 6000 kilometers in 5 hours with the wind
Let,
x be the speed of plane in still air
y be the rate of wind
Combined speed against the wind = x - y
Combined speed with the wind = x+y
Speed = [tex]\frac{Distance}{Time}[/tex]
x-y= [tex]\frac{5040}{6} = 840[/tex]
x - y = 840 Eqn 1
x + y = [tex]\frac{6000}{5} = 1200[/tex] Eqn 2
Adding Eqn 1 and 2
x+y+x-y=1200+840
2x=2040
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{2040}{x}\\x=1020[/tex]
Putting x=1020 in Eqn 2
1020+y=1200
y=1200-1020
y=180
Hence,
The rate of plane in still air is 1020 kilometers per hour and rate of wind is 180 kilometers per hour.
