SOLUTION: ok, this one I am having issues with. It is a word problem dealing with rational equations. A pilot can travel 400 miles with the wind in the same amount of time as 336 miles ag

Question 418281: ok, this one I am having issues with. It is a word problem dealing with rational equations.
A pilot can travel 400 miles with the wind in the same amount of time as 336 miles against the wind. Find the speed of the wind if the pilot's speed in still air is 230 miles per hour
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
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.
.
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.
.
The two distances are:
400 miles when the ground speed is 230 + s.
336 miles when the ground speed is 230 - s.
.
Recall the time, t, is the same in both cases.
So, we can set up the equation we need to solve as follows:

.
We can cross multiply to get to:

.
Multiplying to eliminate the parentheses.
.

.
Adding 336s to both sides.
.

.
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!
.
But how?
.
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.

Divide both sides by 250.

.
How long does it take to go 336 miles at 210 mph?

Divide both sides by 210.

.
So our answer is consistent.
.
Remember to check the question to be sure to answer it.
"The wind speed is 20 mph."
.
Done.
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