Answers:
- rate of the plane in still air = 770 km per hour
- rate of the wind = 130 km per hour
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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.
