Question

An airplane flies into the wind for 5 hours, traveling 900 miles. The airplane then

turns around and flies with the wind, returning to its starting place in 4 hours.
This can be modeled by the following system of equations, where (s) is the speed
of the plane with no wind and (w) is the speed of the wind.
5(s-w)=900
4(s+w) = 900
What is the speed of the wind in miles per hour?

Answer 1

22.5 miles per hour

Explanation:

Given system of equations

5(s-w)=900

4(s+w)=900

Set equations equal to each other

5(s-w)=4(s+w)

5s-5w=4s+4w

s-5w=4w

s=9w

Solve for w using the substitution s=9w

4(s+w)=900

4(9w+w)=900

4(10w)=900

40w=900

w=22.5

Therefore, the speed of the wind is 22.5 miles per hour