SOLUTION: At full speed, an airplane can travel 4500 miles with the wind in 6 hours, but it requires 10 hours to travel the same distance against the wind. What is the wind speed in miles pe

Question 415704: At full speed, an airplane can travel 4500 miles with the wind in 6 hours, but it requires 10 hours to travel the same distance against the wind. What is the wind speed in miles per hour?
Found 2 solutions by htmentor, Theo:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let s=speed of plane, w=speed of wind
Then (1) s + w = 4500 mi/6 hr = 750 mph (with the wind)
And (2) s - w = 4500mi/10 hr = 450 mph (against the wind)
Subtracting (2) from (1) gives 2s = 300 mph or s = 150 mph
So wind speed = 150 miles per hour
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance

w = speed of the wind
r = speed of the airplane
r+w = speed of the airplane with the wind
r-w = speed of the airplane against the wind.

with the wind, the equation becomes:

6*(r+w) = 4500

against the wind, the equation becomes:

10*(r-w) = 4500

since they both equal to 4500, then they both equal to each other, so we get:

6*(r+w) = 10*(r-w)

simplify to get:

6r + 6w = 10r - 10w

subtract 6r from both sides of this equation and add 10w to both sides of this equation to get:

4r = 16w

divide both sides of this equation by 4 to get:

r = 4w

substitute 4w for r in either equation to solve for w.

first equation is:

6*(r+w) = 4500

substitute to get:

6 * (4w + w) = 4500

combine like terms to get:

6 * 5w = 4500

solve to get:

w = 4500 / 30 = 150

since r = 4w, then r must be equal to 600

you have r = 600 and w = 150

substitute in the second equation to see if that equation is true.

10*(600-150) = 4500

combine like terms to get 10*(450) = 4500 which is true.

the values of r and w are good.

the plane travels at 600 miles per hour and the wind travels at 150 miles per hour.

the answer to the question is that the wind speed is 150 miles per hour.

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