SOLUTION: With a head wind, Ethan's plane traveled 1000 miles in 4 hours. With the same wind as a tail wind, the return trip took 3 hours 20 minutes. Find the plane's air speed and the wind

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Question 920302: With a head wind, Ethan's plane traveled 1000 miles in 4 hours. With the same wind as a tail wind, the return trip took 3 hours 20 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 given speed =y mph
against wind speed given 4 hours
with wind speed given 3 1/ 3 hours

Distance against 1000 miles distance with 1000 miles
t=d/r against wind speed given -
1000 / ( x - y )= 4
4 ( x - y ) = 3 1/ 3
4 x - 4 y = 1000 ....................1

1000 / ( x + y )= 10/ 3
3 1/ 3 ( x + y ) = 1000
10x + 10y = 3000
x+y=300 ...............2
Multiply (2) by 4

we get
4x -4 y = 1200
add to (1)
8x=2200
/8
x = 275 mph
plug x in the eqution to get y
x+y=300
275+y=300
y=300-275
y = 25.00
plane speed 275.00 mph
wind speed given speed 25.00 mph