SOLUTION: With a tail wind, a plane traveled 800mi in 5hrs. With a head wind, the plane traveled the same distance in 8hrs. Find the plane's air speed and the speed of the wind. Assume that

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Question 91810: With a tail wind, a plane traveled 800mi in 5hrs. With a head wind, the plane traveled the same distance in 8hrs. Find the plane's air speed and the speed of the wind. Assume that both were constant
Answer by mathispowerful(115) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the plane speed is x, the wind speed is y
5(x + y) = 800
8(x - y) = 800
Solve this system of equations:

Multiply the first equation by 8; second equation by 5,
we have 40(x + y) = 6400
40(x - y) = 4000
40x + 40y = 6400
40x - 40y = 4000
add these 2 equations: 80x = 10400, solve for x , x = 130
Plug x = 130 into one of the above equations to solve y:
40%2A130+%2B+40y = 6400
40y = 6400 - 5200
y = 30
So the speed of plane is 130, the speed of the wind is 30