Aplane travels at a speed of 190 mph in still air. flying with a tailwind, the plane is clocked over a distance of 500 miles. flying against a headwind, it takes 1 hour longer to complete the return trip. what was the wind velocity?

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 =

Now, With the wind

190 + w =  

or, t =

And Against the wind

190 - w =

Solving the equation

I.e ( 190 - w ) ( t + 1 ) = 500

or, ( 190 - w ) ( + 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 =

Or, w =

Or, w =

∴ w = ,  

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

step-by-step explanation:

at each of the parallel lines adjacent angles are supplementary. the angles have special names identifying their positions with respect to the parallel lines and transversal. they are corresponding angles, alternate interior angles, or alternate exterior angles. an angles is congruent to its matched angle.