SOLUTION: a plane left an airport and flew with the wind for 4 hours, covering 2,000 kilometers. it then returned over the same route against the same wind in 5 hours. find the rate of the p
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Question 539555: a plane left an airport and flew with the wind for 4 hours, covering 2,000 kilometers. it then returned over the same route against the same wind in 5 hours. find the rate of the plane in still air and the speed of the wind. Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! a = airspeed of the plane in calm air
w = wind speed
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ground speed with a tailwind = a+w
ground speed with a headwind = a-w
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d = 2000 km
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(a+w) *4 hr = 2000 km
a+w = 500 km/hr
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(a-w) *5 hr = 2000 km
a-w = 400 km/hr
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a + w = 500
a - w = 400
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2a = 900
a = 450
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a+w = 500
w = 50
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Check the distances traveled over the given times.
(450+50) km/hr * 4 hr = 2000 km
(450-50) km/hr * 5 hr = 2000 km
Correct
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Answer: The rate of the plane in calm air is 450 km/hr. The wind speed is 50 km/hr.
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Done.
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