SOLUTION: A plane flies 720 miles with the wind in 3 hours. the return trip (against the wind) takes 4 hours. what is the speed of the wind and the speed of the plane in still air
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Question 1112308: A plane flies 720 miles with the wind in 3 hours. the return trip (against the wind) takes 4 hours. what is the speed of the wind and the speed of the plane in still air Found 3 solutions by josgarithmetic, ikleyn, josmiceli:Answer by josgarithmetic(39616) (Show Source):
= 240 = u + v is the effective speed with the wind.
= 180 = u - v is the effective speed against the wind.
So, you have this system of 2 eqs in 2 unknowns
u + v = 240 (1)
u - v = 180 (2)
where "u" is the speed of the plane at no wind; "v" is the speed of the wind.
To solve the system, add the equations. You will get
2u = 240+180 = 420 ====> u = = 210.
So, 210 mph is the speed of the plane at no wind.
Now from eq(1) v = 210-180 = 30 mph is the speed of the wind.
Solved.
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It is a typical "tailwind and headwind" word problem.
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
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Equation for flying with the wind:
(1)
Equation for flying against the wind:
(2)
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(1)
Multiply both sides by
(1)
and
(2)
Multiply both sides by
(2)
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Add (1) and (2)
(1)
(2)
---------------------------
and
(1)
(1)
(1)
(1)
(1)
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The wind speed is 30 mi/hr
The speed of the plane in still air is 210 mi/hr
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check answer:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK
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