Respuesta :
Answer:
The velocity of wind is 34.88 miles per hour
Step-by-step explanation:
Given as :
The velocity of plane = 190 miles per hour
Let The velocity of wind = w miles per hour
The distance cover by plane = 500 miles
The time taken to cover 500 miles with the wind = t hours
The time taken to cover 500 miles against the wind = ( 1 + t ) hours
Now , Speed = [tex]\dfrac{\terxtrm Distance}{\textrm Time}[/tex]
Now, With the wind
190 + w = [tex]\dfrac{\terxtrm 500}{\textrm t}[/tex]
or, t = [tex]\dfrac{\terxtrm 500}{\textrm 190 + w}[/tex]
And Against the wind
190 - w = [tex]\dfrac{\terxtrm 500}{\textrm ( t + 1 )}[/tex]
Solving the equation
I.e ( 190 - w ) ( t + 1 ) = 500
or, ( 190 - w ) ( [tex]\dfrac{\terxtrm 500}{\textrm 190 + w}[/tex] + 1 ) = 500
Or, ( 190 - w ) [ 500 + ( 190 + w ) ] = 500 ( 190 + w )
Or, 500 × 190 + 190 × ( 190 + w ) - 500 w - w × ( 190 + w ) = 500 × 190 + 500 w
or, 190 × ( 190 + w ) - 500 w - w × 190 - w² = 500 w
or, 190² + 190 w - 500 w - 190 w - w² = 500 w
or, - w² - 1000 w + 190² = 0
Or , w² + 1000 w - 36100 = 0
Solving this quadratic equation
w = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
Or, w = [tex]\frac{-1000\pm \sqrt{1000^{2}-4\times 1\times (-36100)}}{2\times 1}[/tex]
Or, w = [tex]\frac{-1000\pm \sqrt{1144400}}{2}[/tex]
∴ w = [tex]\frac{-1000 + 1069.76}{2}[/tex] , [tex]\frac{-1000 - 1069.76}{2}[/tex]
or, w = 34.88 mph , - 1034.88 mph
So, The wind velocity = w = 34.88 mph
Hence The velocity of wind is 34.88 miles per hour Answer
