Question 147410: An airplane flew for 3 hours with a tail wind of 40 km/hr. The return flight against the same wind took 4 hours. Find the speed of the airplane in still air.
Answer by Electrified_Levi(103)   (Show Source):
You can put this solution on YOUR website! Hi , Hope I can help
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An airplane flew for 3 hours with a tail wind of 40 km/hr. The return flight against the same wind took 4 hours. Find the speed of the airplane in still air.
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The airplane flew the same amount of miles each way.
Distance= (Rate)(Time)
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We know the Time for each way, 3 hours with the wind, and 4 hours against the wind
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We know that "x" is how fast it is going in still air.
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Since the wind is adding to the speed on the first trip, we know that the speed is equal to (x+40)
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On the return trip the plane is going against the wind, and decreasing the speed of the airplane, so the speed is equal to (x-40)
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Now that we know both the time and the rate, we can solve it.
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Distance = (Rate)(Time), or
(Rate)(Time)=(Rate)(Time)
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Now we can put numbers in
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(x + 40)(3) = (x - 40)(4)
3(x + 40) = 4(x - 40)
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We will use distribution property,
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3x + 120 = 4x - 160
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We will now subtract 3x from both sides
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0 + 120 = x - 160
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We will add 160 to both sides
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160 + 120 = x + 0
x = 280
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The airplane is going 280 km/hr. in still air.
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You can check by replacing "x" with "280"
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3(x + 40) = 4(x - 40)
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3(280 + 40) = 4(280 - 40)
3(320) = 4(240)
(960 = 960)
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The airplane also went 960 miles, each way.
1,920 miles all together.
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Hope I helped, Levi
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