Given:
A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind.
Pilot's speed in still air is 315 miles per hour.
To find:
The speed of the wind.
Solution:
Let the speed of wind be x miles per hour.
Speed with wind = 315+x miles per hour
Speed against wind = 315-x miles per hour
We know that,
[tex]Time=\dfrac{Distance}{Speed}[/tex]
According to the question,
[tex]\dfrac{450}{315+x}=\dfrac{360}{315-x}[/tex]
Divide both sides by 90.
[tex]\dfrac{5}{315+x}=\dfrac{4}{315-x}[/tex]
By cross multiplication, we get
[tex]5(315-x)=4(315+x)[/tex]
[tex]5(315)-5x=4(315)+4x[/tex]
[tex]5(315)-4(315)=4x+5x[/tex]
[tex](5-4)315=9x[/tex]
Divide both sides by 9.
[tex]\dfrac{(1)315}{9}=x[/tex]
[tex]35=x[/tex]
Therefore, the speed of wind is 35 miles per hour.
