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If a plane can travel 480 miles per hour with the wind and 420 miles per hour against the​ wind, find the speed of the wind and the speed of the plane in still air.

Respuesta :

oladayoademosu

a. The speed of the wind is 30 mph

b. The speed of the plane in still air is 450 mph

Let

  • V = speed of plane in still air and
  • v = speed of wind.

The required equations

Since the plane can travel 480 miles per hour with the wind, we have that

V + v = 480 (1)

Also, the plane travels 420 miles per hour against the​ wind, we have that

V - v = 420 (2)

a. Speed of the wind

The speed of the wind is 30 mph

subtracting equations (1) and (2), we have

V + v = 480 (1)

-

V - v = 420 (2)

2v = 60

v = 60/2

v = 30 mph

So, the speed of the wind is 30 mph

b. Speed of the plane in still air

The speed of the plane in still air is 450 mph

Substituting v into equation (1), we have

V + v = 480 (1)

V + 30 = 480

V = 480 - 30

V = 450 mph

So, the speed of the plane in still air is 450 mph

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