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On a certain day, Donnie observes the wind is blowing at 2 miles per hour. A bird nesting near Donnie's house flies three quarters of a mile down the road (in the direction of the wind), turns around, and returns exactly 12 minutes later. What is the airspeed of the bird? (Here, 'airspeed' is the speed the bird can fly in still air.)

Respuesta :

Answer:

Air speed of bird is [tex]4.17[/tex] mph

Explanation:

let the speed of the bird in still air be "X"

Speed of the bird when it flies in the direction of flow of wind [tex]= X+2[/tex]

Speed of the bird when it flies in the opposite direction of flow of wind [tex]= X-2[/tex]

The total time taken is equal to [tex]12[/tex] minutes

[tex]= \frac{12}{60} \\= \frac{1}{5}[/tex] hours

The distance in miles is equal to [tex]\frac{3}{4}[/tex] [tex]= 0.75[/tex] miles

  [tex]\frac{0.75}{X+2} + \frac{0.75}{X-2} = \frac{1}{5}[/tex]

On solving the above equation, we get -

[tex]2 X = (X^2 -4)*\frac{1}{0.75 *5} \\X^2 -4 -0.75 X =0\\X = 4.17[/tex]

Air speed of bird is [tex]4.17[/tex] mph

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