SOLUTION: a light plane flew from its home base to an airport 255 miles away. with a headwind the trip took 1.7 hours the return trip with a tailwind took 1.5 hours. Find the average air s

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: a light plane flew from its home base to an airport 255 miles away. with a headwind the trip took 1.7 hours the return trip with a tailwind took 1.5 hours. Find the average air s      Log On


   

Question 24144: a light plane flew from its home base to an airport 255 miles away. with a headwind the trip took 1.7 hours the return trip with a tailwind took 1.5 hours. Find the average air speed of the plane and the average wind speed?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of the plane be x
Let the speed of the wind be y

1.7(x-y)=255 --->1.7x-1.7y=255 (equation 1)
1.5(x+y)=255 --->1.5x+1.5y=255 (equation 2)

Multiply equation 1 by 15 and equation 2 by 17 to get:
25.5x-25.5y=3825 (add)
25.5x+25.5y=4335 (add)
----------------
51x=8160 (divide both sides by 51)
x=160

Solve for y:
1.7(160)-1.7y=255
272-1.7y=255
-1.7y=--17
y=10

Hence the speed of the plane is 160mi/h and the speed of the wind is 10mi/h.
Paul.