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.

Question

23-02-2022
Mathematics

contestada

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.

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oladayoademosu oladayoademosu · Answer 1 · 2022-03-08T10:15:03+01:00

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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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 :

The required equations

a. Speed of the wind

b. Speed of the plane in still air

Otras preguntas

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.