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A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is 4 mph. What is the speed of the flying carpet in still air?

Respuesta :

danielgeyfman

Answer:

[tex]15.2~mph[/tex]

Step-by-step explanation:

Let the time flown by the flying carpet be [tex]t[/tex]. Then, we have that [tex](2.4)/t=(1.4)/t+2*4[/tex].

We multiply both sides of the equation by [tex]t[/tex] to get [tex]2.4=1.4+8t[/tex].

We subtract [tex]1.4[/tex] from both sides to get [tex]1=8t[/tex].

We divide both sides of the equation by [tex]t=1/8[/tex].

We know that the speed of the flying carpet in still wind is the average of the rates of the speed of the flying carpet with the wind and against the wind.

The speed with wind is [tex](2.4)/(1/8)=19.2[/tex]mph.

The speed against wind is [tex](1.4)/(1/8)=11.2[/tex]mph.

The speed in still wind is [tex](19.2+11.2)/2=(30.4)/2=15.2[/tex].

Therefore, the answer is [tex]\boxed{15.2~mph}[/tex] and we're done!

raphealnwobi

The speed of the flying carpet in still air is 15.2 mph

Let x represent the speed of the flying carpet in still air, and t represent the time.

Speed = distance/time

Since the wind speed is 4 mph, hence:

When flying with the wind:

x + 4 mph = 2.4/t     (1)

When flying against the wind:

x - 4 mph = 1.4/t     (2)

Dividing equation 1 by 2 gives:

(x + 4) / (x - 4) = 2.4/1.4

1.4x + 5.6 = 2.4x - 9.6

x = 15.2 mph

The speed of the flying carpet in still air is 15.2 mph

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