SOLUTION: A plane flies 500 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is 28mph, what is the speed of the plane in still air?

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Question 56780: A plane flies 500 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is 28mph, what is the speed of the plane in still air?
Found 3 solutions by Nate, funmath, stanbon:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
rate of air = a
going with wind ~> 28 + a
going against wind ~> 28 - a
Rate*Time = Distance
Distance/Rate = Time
500/(28 + a) = 340/(28 - a) Since the times are equivalent, you would would equal them together.
500(28 - a) = 340(28 + a)
14000 - 500a = 9520 + 340a
-840a = -4480
a = 16/3
Speed in still air is about 5.3333 mi/hr. We do not know the time measurement, but we can guess or propose it is in hours. The time comes to 15 hours.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
A plane flies 500 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is 28mph, what is the speed of the plane in still air?
the distance formula is d=rt solve tihs for t and you have: d%2Fr=t
Both our t's are the same so we're going to let t=t or d/r with the wind =d/r against the wind.
Let the rate of the plane be:x
Then the rate with the wind is: x+28
And the rate against the wind is: x-28
The distance with the wind is:500
The distance against the wind is: 340
The problem to solve is:
500%2F%28x%2B28%29=340%2F%28x-28%29
500%28x%2B28%29%28x-28%29%2F%28x%2B28%29=340%28x%2B28%29%28x-28%29%2F%28x-28%29

500%28x-28%29=340%28x%2B28%29
500x-14000=340x%2B9520
-340x%2B500x-14000=-340x%2B340x%2B9520
160x-14000=9520
160x-14000%2B14000=14000%2B9520
160x=23520
160x%2F160=23520%2F160
x=147
The rate of the plane in still air is: 147 mph
Happy Calculating!!!

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A plane flies 500 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is 28mph, what is the speed of the plane in still air?
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Let speed of the plane be p mph.
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With the wind DATA:
distance= 500 miles ; rate = (p+28) mph ; time =d/r =500/(p+28) hrs.
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Against the wind DATA:
distance=340 miles ; rate = (p-28) mph ; time = d/r = 340/(p-28) hrs
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EQUATION:
time with = time against
500/(p+28) = 340/(p-28)
25(p-28) = 17(p+28)
25p-700 = 17p+476
8p=1176
p=147 mph (speed of the plane in still air)
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Cheers,
Stan H.