SOLUTION: A plane flying with the wind went 350 miles in 2 hours. The return trip, flying against the wind, took 2.8 hours. Find the rate of the plane in calm air and the rate of the wind.

Question 511445: A plane flying with the wind went 350 miles in 2 hours. The return trip, flying against the wind, took 2.8 hours. Find the rate of the plane in calm air and the rate of the wind.

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
d = rt is the distance equation.
.
a = aircraft speed
w = wind speed
.
Flying with the wind, the ground speed = a+w
.
(a+w) * 2 = 350
a + w = 175
a = 175-w
.
Flying against the wind, the ground speed = a-w
.
(a-w) * 2.8 = 350
.
substitute a = (175-w)
.
(175-w -w) * 2.8 = 350
.
175 -2w = 125
.
-2w = -50
.
w = 25 = wind speed
.
substitute
.
a + w = 175
a + 25 = 175
a = 150 = aircraft speed
.
Check the answer.
.
(150-25)*x = 350
125x = 350
x = 2.8
Correct.
.
Answer: The aircraft flies 150 mph and the wind is 25 mph.
.

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