SOLUTION: A plane can fly at a rate of 215 mph in calm air. Traveling with the wind the plane flew 750 miles in the same amount of time that it flew 540 miles againstthe wind. Find the rate

Question 966100: A plane can fly at a rate of 215 mph in calm air. Traveling with the wind the plane flew 750 miles in the same amount of time that it flew 540 miles againstthe wind. Find the rate of the wind.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!

Let x be the wind speed (=rate), in .
Then the speed of the plane when flying with the wind is 215 + x .
The speed of the plane when flying against the wind is 215 - x .
The plane covers the distance of 750 miles in    flying with the wind.
The plane covers the distance of 540 miles in    flying against the wind.

So, you have an equation = to find .

Multiply both sides by . You will get

750*(215-x) = 540*(215+x).

Divide both sides by 30. You will get

25*(215-x) = 18*(215+x).

Open parentheses; collect the x-terms in the right side; collect the constant terms in the left side:

25*215 - 18*215 = 18*x + 25*x, or

7*215 = 43x.

Divide both sides by 43. You will get
x = 7*5 = 35.

Answer. The rate of wind is 35 .

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
r=215 miles per hour, speed without wind
w= unknown wind speed
v=750 miles
u=540 miles
t=amount of time, same for both trip situations

This is analyzed and solved purely symbolically because other questions have occurred like this but with different values or different examples of this same form.

_____________________rate___________time___________distance
WITHWIND_____________r+w_____________t______________v
AGAINSTW_____________r-w_____________t______________u

The variables w and t can be solved; but the question asks for w.

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