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

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
.
ground speed with a tailwind = a+w
ground speed with a headwind = a-w
.
d = 2000 km
.
(a+w) *4 hr = 2000 km
a+w = 500 km/hr
.
(a-w) *5 hr = 2000 km
a-w = 400 km/hr
.
a + w = 500
a - w = 400
------------
2a = 900
a = 450
.
a+w = 500
w = 50
.
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
.
Answer: The rate of the plane in calm air is 450 km/hr. The wind speed is 50 km/hr.
.
Done.
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