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Flying against the wind, a jet travels miles in hours. Flying with the wind, the same jet travels miles in hours. What is the rate of the jet in still air and what is the rate of the wind

Sagot :

MrRoyalidn

Answer:

Velocity in still air: 760 mi/ hr

Velocity against the wind: 210 mi/ hr

Step-by-step explanation:

Given

See attachment for complete question

Required

The rate in still air

The rate of the wind

From the question, the velocity (v) against the wind is:

[tex]v =\frac{distance}{time}[/tex]

[tex]v =\frac{3040}{4}[/tex]

[tex]v_1 =760mi/hr[/tex]

The velocity with the wind is:

[tex]v_2 = \frac{8260}{7}[/tex]

[tex]v_2 = 1180mi/hr[/tex]

Let:

[tex]x \to[/tex] velocity in still air

[tex]y \to[/tex] velocity of the wind

So, we have:

[tex]x - y = 760[/tex]

[tex]x + y = 1180[/tex]

Add both equations

[tex]x + x -y + y = 760 + 1180[/tex]

[tex]2x = 1940[/tex]

Divide by 2

[tex]x = 970[/tex]

Substitute [tex]x = 970[/tex] in [tex]x - y = 760[/tex]

[tex]970 - y= 760[/tex]

Make y the subject

[tex]y = 970 - 760[/tex]

[tex]y = 210[/tex]

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