SOLUTION: A small airplane travels between two cities A and B, 600 miles apart. When going from city A to city B, the plane encounters headwind and reaches city B four hours after leaving. W

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: A small airplane travels between two cities A and B, 600 miles apart. When going from city A to city B, the plane encounters headwind and reaches city B four hours after leaving. W      Log On

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Question 32275: A small airplane travels between two cities A and B, 600 miles apart. When going from city A to city B, the plane encounters headwind and reaches city B four hours after leaving. With the wind the return trip takes three hours.
What is the airspeed of the plane? What is the speed of the wind?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of the wind be y
Let the speed of the plane be x
two eqautions:
3(x+y)=600---->3x+3y=600
Solve for y:
y=200-x
SEcond EQuation:
4(x-y)=600 ---->4x-4y=600
Subsitute foor y:
4x-4(200-x)=600
4x+4x-800=600
8x=1400
x=175
y=200-175
y=25.
Hence, the speed of the plane is 175mph, and the speed of the wind is 25mph.
Paul.