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Joe flew 300 miles with the wind in two hours.
After flying against the wind for two hours, he had made 270 miles of the return trip.
Find the wind speed and the speed of the plane in still air.
Let s = the speed in still air
Let w = the speed of the wind
(s-w) = effective speed against the wind
(s+w) = effective speed with the wind
write a distance equation for each way (dist = time * effective speed)
2(s+w) = 300
2(s-w) = 270
Simplify both equations by dividing both sides by 2, results
s + w = 150
s - w = 135
--------------adding eliminates w, find s
2s = 285
s = 285/2
s = 142.5 mph, plane speed in still air
142.5 + w = 150
w = 150 - 142.5
w = 7.5 mph is the speed of the wind
YOu can check these solution yourself in the original equations