Answer :
Answer:
Speed of the wind = 30 mi\hr
Explanation:
Let x be the speed of the wind
Given:
Speed of the plane without air [tex]s = 150\ mi\hr[/tex]
Speed of the plane with air [tex]s_{1}= (150 + x)\ mi\hr[/tex]
Speed of the plane against air [tex]s_{2} = (150 - x)\ mi\hr[/tex]
Plane flew with the wind [tex]d_{1}=300\ mi[/tex]
Plane flew against the wind [tex]d_{2}=200\ mi[/tex]
We need to find the speed of the wind.
Solution:
Using speed formula as given below.
[tex]Speed=\frac{distance}{time}[/tex] -----------(1)
Speed of the plane with air,
Substitute [tex]distance=300\ mi[/tex], [tex]speed= (150 + x)\ mi\hr[/tex] and [tex]time = t[/tex] in equation 1.
[tex](150+x)=\frac{300}{t}[/tex]
[tex]t(150+x)=300 --------(2)[/tex]
Similarly, speed of the plane against air
Now, we substitute distance [tex]d_{2}=200\ mi[/tex], speed [tex]s_{2} = (150 - x)\ mi\hr[/tex] and [tex]time = t[/tex] in equation 1.
[tex](150-x)=\frac{200}{t}[/tex]
[tex]t(150-x)=200 --------(3)[/tex]
Now, we divide equation 2 by equation 3.
[tex]\frac{t(150+x)}{t(150-x)} =\frac{300}{200}[/tex]
t and t cancelled.
[tex]\frac{(150+x)}{(150-x)} =\frac{3}{2}[/tex]
Applying cross multiplication rule.
[tex]2(150+x)=3(150-x)[/tex]
[tex]300+2x=450-3x[/tex]
[tex]2x+3x=450-300[/tex]
[tex]5x=150[/tex]
[tex]x=\frac{150}{5}[/tex]
x = 30 mi\hr
Therefore, the speed of the wind is 30 miles per hour.