SOLUTION: need a system of equations for this prob: an airplane flew 4 hours against a wind of 40 km/h. on return he was flowing with the wind and flight was 3 hours. whats speed of airplane

Question 62429: need a system of equations for this prob: an airplane flew 4 hours against a wind of 40 km/h. on return he was flowing with the wind and flight was 3 hours. whats speed of airplane in still air.
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
An airplane flew 4 hours against a wind of 40 km/h. On return he was flowing with the wind and flight was 3 hours. What's speed of airplane in still air.
:
, d=distance, r=rate or speed, and t=time
Let the speed in still air be: x
Let the distance be:y
Then the trip against the wind can be modeled by the equation:
y=4(x-40)
The return trip can be modeled by (assuming that the wind didn't change speeds:
y=3(x+40)
Therefore, your system of equations is:
y=4(x-40)
y=3(x+40)
:
If you needed to find the speed of the airplane in still air, you'd let the two y's equal each other.
4(x-40)=3(x+40)
4x-160=3x+120
4x-3x-160=3x-3x+120
x-160=120
x-160+160=120+160
x=280
The speed in still air is: x=280 km/h
(You didn't ask, but for fun I thought you'd like to know that the trip was 960 km. Figure that out too if you want.)
Happy Calculating!!!

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