SOLUTION: A light plane flew from its home base to an airport 255 miles away. With a head wind, the trip took 1.7 hours. The return trip with a tail wind took 1.5 hours. Find average airspee

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Question 1010832: A light plane flew from its home base to an airport 255 miles away. With a head wind, the trip took 1.7 hours. The return trip with a tail wind took 1.5 hours. Find average airspeed of the plane and the average windspeed.
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
VARIABLE ASSIGMENTS
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y=1.7 hours        time with the wind
x=1.5 hours        time against the wind
d=255 miles        trip distance
r miles per hour   unknown plane speed without any wind
w miles per hour   speed of the wind


                   speed       time      distance
AGAINST Wind       r-w          y          d
WITH Wind          r+w          x          d


System of equations, system%28%28r-w%29y=d%2C%28r%2Bw%29x=d%29

SOLUTION ALGEBRA STEPS
yr-yw=d
yr=d%2Byw
r=%28d%2Byw%29%2Fy
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substitute into the other equation.
xr%2Bxw=d
x%28d%2Byw%29%2Fy%2Bxw=d
xd%2Fy%2Bxyw%2Fy%2Bxw=d
xd%2Fy%2Bxw%2Bxw=d
2xw%2Bxd%2Fy=d
2xw=d-xd%2Fy
w=%281%2F%282x%29%29%28d-xd%2Fy%29
highlight%28w=d%2F%282x%29-d%2F%282y%29%29-----This can be evaluated using the assigned values.
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Use the formula for w to find a formula for r.
r=%28d%2Byw%29%2Fy
r=%28d%2By%28d%2F%282x%29-d%2F%282y%29%29%29%2Fy
%28d%2Byd%2F%282x%29-yd%2F%282y%29%29%2Fy
%28d%2Byd%2F%282x%29-d%2F2%29%2Fy
d%2Fy%2Bd%2F%282x%29-d%2F%282y%29
d%281%2Fy%2B1%2F%282x%29-1%2F%282y%29%29
d%282x%2F%282xy%29%2By%2F%282xy%29-x%2F%282xy%29%29
highlight%28r=d%28%282x%2By-x%29%2F%282xy%29%29%29------Evaluate using the variable assignments.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A light plane flew from its home base to an airport 255 miles away. With a head wind, the trip took 1.7 hours. The return trip with a tail wind took 1.5 hours. Find average airspeed of the plane and the average windspeed.
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Find the 2 groundspeeds, upwind and downwind.
The plane's airspeed is the average of the 2.
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Windspeed is the difference between airspeed and groundspeed.