Question 834503: Assume that a plane is traveling at a constant speed under unvarying wind conditions. Traveling agaisnt a headwind, the plane takes 4 hours to travel 1540 miles. Traveling with a tail wind, the plane flies 1365 miles in 3 hours. Find the speed of the plane and the speed of the wind.
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website! You probably meant to ask for the solution further down below, starting at "WHAT did you really mean to describe?"-------------
H = speed of plane chosen without wind but during travel opposing the wind
L = speed of plane chosen without wind but during travel along or with the wind
w = speed of wind
Note that I am taking your wording, "Assume that a plane is traveling at a constant speed under unvarying wind conditions" exactly as written. That means the plane travel is the same speed in both directions. YOU HAVE THREE VARIABLES.
______________speed______________time___________distance
AGAINST W_____H-w________________4______________1540
WITH W________L+w________________3______________1365
Further, as stated in the description, if speed is constant for both directions then 
 ;
We can make two more equations based on the data table shown above:
 , and  , which now give a system of three equations in three unknowns.
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(L+w)*3=1365
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The system can be expressed in these simultaneous equations:
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H-L=2w
H-w=385
L+w=455
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Try eliminating for w to get two equations in H and L.
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L+(H-L)/2=455
2L+H-L=2*455
2L+H-L=910
H+L=910
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NO GOOD. H+L cannot be both 910 and 770 at the same time.
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WHAT did you really mean to describe? Did you mean, "both planes travel at constant, but DIFFERENT speeds in each direction"? If THAT is really what you mean, then just assume the plane has a speed r without wind, and try this data arrangement:
Regarding Winde_______speed____________time____________distance
AGAINST_______________r-w______________4_______________1540
WITH__________________r+w______________3_______________1365
TWO EQUATIONS:
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SYSTEM TO SOLVE READY TO SOLVE:
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r-w=385
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r+w=455
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Add the left members and add the right members and this eliminates w for getting a value for r.
This produces first 
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Use either equation of the system to get the value for w.
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