SOLUTION: A plane traveled 644 miles to Austin and back. The trip there was with the wind. It took 7 hours. the trip back was into the wind. The trip took 14 hours. What is the speed of the

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Question 895698: A plane traveled 644 miles to Austin and back. The trip there was with the wind. It took 7 hours. the trip back was into the wind. The trip took 14 hours. What is the speed of the plane in still air? What is the speed of the wind?

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Found 2 solutions by Alan3354, lwsshak3:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
A plane traveled 644 miles to Austin and back. The trip there was with the wind. It took 7 hours. the trip back was into the wind. The trip took 14 hours. What is the speed of the plane in still air? What is the speed of the wind?
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Use d = r*t --> r = d/t to find the 2 groundspeeds.
The plane's airspeed is the average of them.
The windspeed is the difference between airspeed and groundspeed.

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
A plane traveled 644 miles to Austin and back. The trip there was with the wind. It took 7 hours. the trip back was into the wind. The trip took 14 hours. What is the speed of the plane in still air? What is the speed of the wind?
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let x=speed of plane in still air
let c=speed of wind
x+c=speed of plane with wind
x-c=speed of plane into wind
Distance/speed=travel time
..
644/(x+c)=7
644/(x-c)=14
..
7x+7c=644
14x-14c=644
..
14x+14c=1288 (mult. by 2)
14x-14c=644
add
28x=1932
x=69
7c=644-7x
7c=161
c=23
speed of plane in still air=69 mph
speed of wind=23 mph