Answer:
The speed of wind is 75 miles / hour
Step-by-step explanation:
Let's assume
speed of airplane is x miles /hour
speed of wind is y miles /hour
Against wind:
An airplane travels 600 miles against the wind in 4 hours
against wind means resultant speed will be less
so, speed =x-y
total distance traveled in 4 hour is
[tex]=4(x-y)[/tex]
and this has to be equal to 600
[tex]600=4(x-y)[/tex]
Divide both sides by 4
and we get
[tex]x-y=150[/tex]
With wind:
makes the return trip with then same wind in 2 hours
with wind means resultant speed will be more
so, speed =x+y
total distance traveled in 2 hour is
[tex]=2(x+y)[/tex]
and this has to be equal to 600
[tex]600=2(x+y)[/tex]
Divide both sides by 2
and we get
[tex]x+y=300[/tex]
So, we get system of equations
[tex]x-y=150[/tex]
[tex]x+y=300[/tex]
now, we can solve it by adding both equations
[tex]x-y+x+y=150+300[/tex]
[tex]2x=450[/tex]
now, we can solve for x
[tex]x=225[/tex]
now, we can find y by plugging x into any one equation
[tex]225+y=300[/tex]
[tex]y=75[/tex]
So,
The speed of wind is 75 miles / hour
