SOLUTION: When a plane flies from Detroit to Denver it has to fly into the wind and the trip takes 4 hours. On the return trip, it will take only 3.5 hours because the plane is flying with t

Question 809333: When a plane flies from Detroit to Denver it has to fly into the wind and the trip takes 4 hours. On the return trip, it will take only 3.5 hours because the plane is flying with the wind. If the distance between Detroit and Denver is 1120 miles, what was speed of the airplane in still air? What was the speed of the wind?

Found 2 solutions by TimothyLamb, josmiceli:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
s = d / t
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1120/4 = s - w
1120/3.5 = s + w
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280 = s - w
320 = s + w
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280 + w = s
320 = s + w
320 = (280 + w) + w
320 = (280 + w) + w
40 = 2w
Answer:
w = 20
s = 300
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the speed of the plane in still air in mi/hr
Let = the speed of the wind in mi/hr
--------------------
Flying into the wind:
(1)
Flying with the wind:
(2)
-------------------------
(1)
and
(2)
-------------------------
Multiply (1) by and
(2) by and add the equations
(1)
(2)

and,
(1)
(1)
(1)
(1)
The speed of the airplane in still air is 300 mi/hr
The speed of the wind is 20 mi/hr
check:
(2)
(2)
(2)
(2)
You can check other equation

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