SOLUTION: An airplane makes a trip in 3.2 hours flying against the wind. The same airplane makes the trip in 3 hours flying with the wind. If the wind is moving at 7 mph, what is the speed o

Question 910337: An airplane makes a trip in 3.2 hours flying against the wind. The same airplane makes the trip in 3 hours flying with the wind. If the wind is moving at 7 mph, what is the speed of the plane? Please show how you solved the problem as well. Thanks!
Found 2 solutions by richwmiller, rothauserc:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
r*t=d
with the wind
(r+7)*3=d
3*r+21=d
against the wind
(r-7)*3.2=d
3.2*r-7*3.2=d
3.2*r-22.4=d
3.2*r-22.4=3*r+21
0.2r=43.4/0.2
r=217.0 mph rate plane
distance=224.0*3=672.0
distance=210.0*3.2=672.0
check
(217.0+7)*3= (217.0-7)*3.2
224.0*3=210.0*3.2
672.0=672.0
ok

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Use rate(r) * time(t) = distance (d)
we are given t1 = 3.2 hours against the wind,
t2 = 3 hours with the wind and rw of the wind is 7 mph
the distance traveled d is the same for against the wind and with the wind
so we can set our equations = to each other
let r be the speed of the plane, then
(r-7) * 3.2 = (r+7) * 3
3.2r - 22.4 = 3r + 21
subtract 3r from both sides of =
.2r -22.4 = 21
add 22.4 to both sides of =
.2r = 43.4
r = 217 mph
the speed of the plane is 217 mph
check the answer in our equation
(217-7) * 3.2 = (217+7) * 3
672 = 672
our answer checks out ok
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