SOLUTION: An airplane flew for 3 hours with a tail wind of 18 kilometers per hour. The return flight against the wind took 4 hours. Find the rate of the plane in still air.
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Question 423288: An airplane flew for 3 hours with a tail wind of 18 kilometers per hour. The return flight against the wind took 4 hours. Find the rate of the plane in still air. Found 4 solutions by mananth, ikleyn, greenestamps, josgarithmetic:Answer by mananth(16949) (Show Source):
You can put this solution on YOUR website! plane speed =x mph
wind speed 18 mph
time with tail wind 3 hours
time against wind 4 hours
Distance = same
8(x+18) =4(x-18)
8x +144 =4x-72
4x-8x=144-72
x =216 mph plane speed
You can put this solution on YOUR website! .
An airplane flew for 3 hours with a tail wind of 18 kilometers per hour.
The return flight against the wind took 4 hours. Find the rate of the plane in still air.
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The solution in the post by @mananth is irrelevant and inadequate to the problem.
I came to bring a correct solution.
Let x be the rate of the airplane in still air.
Then the rate of the airplane flying with the wind is (x+18) km/h;
the rate of the airplane flying against the wind is (x-18) km/h.
Write the distance equation, saying that the distance is the same with the wind
and against the wind
3(x+18) = 4(x-18) kilometers.
Simplify this equation and find x
3x + 54 = 4x - 72,
54 + 72 = 4x - 3x,
126 = x.
?ANSWER. The rate of the airplane in still air is 126 km/h.
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