SOLUTION: 2 cities are 1980 miles apart. one trip flying into the wind took 5.5 hours, the return trip with the wind took only 4.5 hours. what is the speed of the wind and the plane in still

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Question 761829: 2 cities are 1980 miles apart. one trip flying into the wind took 5.5 hours, the return trip with the wind took only 4.5 hours. what is the speed of the wind and the plane in still air
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the speed of plane in still air and y be the wind speed.
Step 1: Flying into the wind, effective speed = %28x+-+y%29. Distance of 1980 is covered in 5.5 hours. Distance = Speed * time.
So
%28x+-+y%29+%2A+5.5+=+1980 or x+-+y+=+1980%2F5.5+=+360 ---> eqn 1
Step 2: Flying with the wind - effective speed = %28x+%2B+y%29
Applying the same formula distance = speed * time
%28x+%2B+y%29+%2A+4.5+=+1980 or x+%2B+y+=+1980%2F4.5+=+440 --- eqn 2
Step 3:
From eqn 1, x = y + 360. Substituting for x in eqn 2
y+%2B+360+%2B+y+=+440
2%2Ay+=+80 or y+=+40
Step 4:
Since y = 40, x+=+y+%2B+360+=+400
Speed of plane in still air = highlight%28400%29 and wind speed = highlight%2840%29
:)