SOLUTION: an airplane makes a 990 km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hours 20 minutes, and the airplane's speed in still air is 600

Question 825285: an airplane makes a 990 km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hours 20 minutes, and the airplane's speed in still air is 600 km/h. What is the speed of the wind?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
an airplane makes a 990 km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hours 20 minutes, and the airplane's speed in still air is 600 km/h. What is the speed of the wind?
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up-wind DATA: rate = 600-w km/hr ; distance = 990 km ; time = 990/(600-w) hrs.
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down-wind DATA: rate = 600+w km/hr ; distance = 990 km ; time = 990/(600+w) hrs.
----
Equation::
time + time = 3 1/3 = 10/3 hrs
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990/(600-w) + 990/(600+w) = 10/3
-------
3*990(600-w) + 3*990(600+w) = 10(600^2-w^2)
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3*99(600-w) + 3*99(600+w) = 600^2-w^2
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2*3*99*600 = 600^2-w^2
----
w^2 = 3600
w = 60 km/hr (wind speed)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the speed of the wind
Flying with the wind
Let = the flying time flying with the wind
----------------------------------------
with the wind
(1)
against the wind
(2)
---------------------------------
(1)
(2)
---------------------------------------
Substitute (1) into (2)
(2)
(2)
(2)
Multiply both sides by
(2)
(2)
(2)
(2)
(2)
(2)
(2)
The wind speed is 60 km/hr
------------------------
check:
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
(2)
(2) hrs
OK

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