Question

A plane travels at a speed of 165mph in still air. Flying with a tailwind, the plane is clocked over a distance of 850 miles. Flying against a headwind, it takes 1 hour longer to complete the return trip. What was the wind velocity? (Round your answer to the nearest tenth.)

Answer 1

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THE ANSWER IS HERE,

The speed of plane in still air => 165mph.

Let the wind velocity be x.

Then the speed of plane with a tailwind => (165+x)mph.

The speed of plane against headwind => (165-x)mph.

From the question,

$= > \: \frac{850}{x + 165} + 1 = \frac{850}{165 - x}$

$= > \: \frac{850}{165 - x} - \frac{850}{165 + x} = 1$

$= > \: 850( \frac{165 + x - (165 - x)}{ {165}^{2} - {x}^{2} } )$

$= > \: 850( \frac{2x}{27225 - {x}^{2} } ) = 1$

$= > \: {x}^{2} + 1700x - 27225 = 0$

This is quadratic equation, So if we solve this equation.

We get 15.85 & -1715.85

We know that speed never be negative. so the velocity of wind is 15.85mph.

:-)Hope it helps u.