Question 418281
Always start with what you know.  For example, distance = rate * time, d = rt.
For this problem we have two different distances, but the same time.
Dividing d=rt by r we have d/r = t.
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The rate (speed) is 230 in still air.  Flying against the wind, the speed across the ground will be 230 - s, where s is the wind speed.  Flying with the wind, the ground speed will be 230 + s.
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The two distances are:  
400 miles when the ground speed is 230 + s.
336 miles when the ground speed is 230 - s.
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Recall the time, t, is the same in both cases.
So, we can set up the equation we need to solve as follows:
{{{400/(230+s) = 336/(230-s)}}}
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We can cross multiply to get to:
{{{400*(230+s) = 336*(230-s)}}}
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Multiplying to eliminate the parentheses.
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{{{92000 + 400s = 77280 - 336s}}}
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Adding 336s to both sides.
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{{{92000 + 736s = 77280
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Subtacting 92000 from both sides.
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{{{736s = -14720}}
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Dividing both sides by 736.
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{{{s = -20}}}
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With the negative sign, that would mean a head wind, which slows the plane down.  Instead of going 230 mph, it goes 210.  Going the other way, the speed would be 230+20=250 mph.
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Always check your work!
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But how?
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Well, let's go figure out what the time, t, is.  We have to check to make sure this makes sense.
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How long does it take to go 400 miles at 250 mph?
Remember, d=rt.
Substitute what we think we know.
{{{400 = 250t}}}
Divide both sides by 250.
{{{1.6=t}}}
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How long does it take to go 336 miles at 210 mph?
{{{336 = 210t}}}
Divide both sides by 210.
{{{1.6=t}}}
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So our answer is consistent.
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Remember to check the question to be sure to answer it.
"The wind speed is 20 mph."
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Done.