Question 527804
Let v = the velocity of the airplane in still air in miles per hour
Let t = the number of hours the airplane flies
Let d = the distance the airplane flies in miles
28 = wind speed in miles per hour
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General rate, distance formula:
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d = v * t
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500 = (v + 28) * t
300 = (v - 28) * t
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The easiest way to solve this: make both equations equal to the same thing.  The easiest way to do that is to set them = 0.  For example:
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500 = (v + 28) * t can be simplified by subtracting 500 from both sides:
0 = vt + 28t - 500
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300 = (v - 28) * t can be simplified by subtracting 300 from both sides:
0 = vt -28t - 300
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Since both equations are equal to zero, they are equal to each other.  Now we have:
vt + 28t - 500 = vt - 28t - 300
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We can continue to simplify:
- First subtract the vt term from both sides:
28t - 500 = -28t -300
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- Then add 28t to both sides:
56t - 500 = -300
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- Then add 500 to both sides:
56t = 200
t = 200/56
t = ~3.57 hrs
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We now take value for t and substitute it back into any of our original equations to solve for v.  After that, we will check our work:
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500 = vt + 28t
500 = 3.57v + 28(3.57)
500 = 3.57v + 100
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Subtract 100 from both sides:
400 = 3.57v
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Divide both sides by 3.57:
v = 112
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This is the answer to the problem.  All we need to do is to check our work.
300 = vt - 28t
300 = (112)(3.57) - 28(3.57)
300 = 400 - 100
300 = 300 checks
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cheers,
Lee