Answer:
The speed of air is 526.22 mi/h
Explanation:
Given that
Distance = 2300 mi
Velocity of wind ,U=65 m/h
Lets take velocity of plane = V
When plane is moving from A to B then resultant velocity of pane = V-65 m/h
Lets take time taken to plane when plane is moving from A to B = t hr
We know that
Distance = Velocity x time
2300 = (V-65) x t
t = 2300/ (V-65) ------------1
When plane is moving from A to B then resultant velocity of pane = V+65 m/h
Time taken by plane from B to A = t -1.08 hr ( 65 min = 1.08 hr)
2300 = (V+65) x (t - 1.08)
[tex]t=1.08+\dfrac{2300}{V+65}[/tex] -------------2
Now from equation 1 and 2
[tex]\dfrac{2300}{V-65}=1.08+\dfrac{2300}{V+65}[/tex]
[tex]\dfrac{2300}{V-65}-\dfrac{2300}{V+65}=1.08[/tex]
[tex]2300\left (\dfrac{1}{V-65}-\dfrac{1}{V+65}\right)=1.08[/tex]
[tex]2300\left (\dfrac{2\times 65}{V^2-65^2}\right)=1.08[/tex]
[tex]V^2=276,916.85[/tex]
V=526.22 mi/h
The speed of air is 526.22 mi/h
