Question

Im gonna fail omg someone help ive been asking for half an hour now.

Flying against the wind, an airplane travels 3200 kilometers in 5 hours. Flying with the wind, the same plane travels 6300 kilometers in 7 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Answers:

• rate of the plane in still air = 770 km per hour
• rate of the wind = 130 km per hour

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Step-by-step explanation:

p = speed of the plane in still air (i.e. without any wind)

w = speed of the wind

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If the plane flies against the wind, then it slows down from p to p-w

distance = rate*time

3200 = (p-w)*5

3200/5 = p-w

p-w = 640

p = 640+w

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If the plane flies with the wind, then it gets a speed boost going from p to p+w

distance = rate*time

6300 = (p+w)*7

6300/7 = p+w

900 = p+w

Now plug in p = 640+w and solve for w

900 = p+w

900 = 640+w+w

900 = 640+2w

2w+640 = 900

2w = 900-640

2w = 260

w = 260/2

w = 130

The wind is moving at a speed of 130 km per hour

p = 640+w = 640+130 = 770

The plane moves at a speed of 770 km per hour if there isn't any wind.