SOLUTION: An airplane flies 400 miles against a headwind in 2 hours. The return trip with the same wind as a tailwind, takes 1 hour and 40 minutes. Find the plane's air speed and the wind sp

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An airplane flies 400 miles against a headwind in 2 hours. The return trip with the same wind as a tailwind, takes 1 hour and 40 minutes. Find the plane's air speed and the wind sp      Log On


   

Question 903939: An airplane flies 400 miles against a headwind in 2 hours. The return trip with the same wind as a tailwind, takes 1 hour and 40 minutes. Find the plane's air speed and the wind speed.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Plane speed =x mph
wind speed =y mph
against wind 2 hours
with wind 1 2/3 hours

Distance against 400 miles distance with 400 miles
t=d/r against wind -
400 / ( x - y )= 2
2 ( x - y ) = 1 2/ 3
2 x - 2 y = 400 ....................1

400 / ( x + y )= 1 2/ 3
1 2/ 3 ( x + y ) = 400
1 2/ 3 x + 1 2/ 3 y = 400 ...............2
Multiply (1) by 1 2/ 3
Multiply (2) by 2
we get
3 1/ 3 x + -3 1/ 3 y = 666 2/ 3
3 1/ 3 x + 3 1/ 3 y = 800
6 2/ 3 x = 1466 2/ 3
/ 6 2/ 3
x = 220 mph

plug value of x in (1) y
2 x -2 y = 400
440 -2 -440 = 400
-2 y = 400
-2 y = -40 mph
y = 20
Plane speed 220 mph
wind speed 20 mph

m.ananth@hotmail.ca