SOLUTION: A plane flew 400 miles eastward with a tail wind and made the trip in 2 hours. It returned with a heads wind and the trip took 3 hours and 20 minutes. Find the speed of the plane

Question 330526: A plane flew 400 miles eastward with a tail wind and made the trip in 2 hours. It returned with a heads wind and the trip took 3 hours and 20 minutes. Find the speed of the plane and the wind. What is the formula for wind speed?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A plane flew 400 miles eastward with a tail wind and made the trip in 2 hours. It returned with a heads wind and the trip took 3 hours and 20 minutes. Find the speed of the plane and the wind. What is the formula for wind speed?
let speed of plane in still air be x mph
speeed of wind be y mph
..
distance 400 miles with tail wind
time = 400/x+y
2=400/x+y
2x+2y=400
divide by 2
x+y=200...................1
..
time = distance /speed (with head wind)
10/3 = 400/ x-y
10x-10y=3*400
10x-10y=1200
x-y=120....................2
add equation 1 & 2
x+y+x-y=200+120
2x=320
x=160 mph speed of plane in still air
..
x+y=200
plug value of x
160+y= 200
y=200-160
y=40 speed of wind

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