SOLUTION: Please help me. A hawk can fly 300 miles in 8 hours with the wind. Flying against the wind, the hawk covers only one-third of the distance in 7 hours. What is the rate of the wi

Question 317393: Please help me. A hawk can fly 300 miles in 8 hours with the wind. Flying against the wind, the hawk covers only one-third of the distance in 7 hours. What is the rate of the wind?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Please help me. A hawk can fly 300 miles in 8 hours with the wind. Flying against the wind, the hawk covers only one-third of the distance in 7 hours. What is the rate of the wind?
.
Let w = rate of wind
and y = speed of hawk w/o wind
.
Applying distance formula of d=rt
we have
8(x+w) = 300 (equation 1)
and
7(x-w) = (1/3)300 (equation 2)
.
Solve equation 1 for x:
8(x+w) = 300
x+w = 300/8
x = 300/8 - w
.
Plug the above into equation 2 and solve for w:
7(x-w) = (1/3)300
7(x-w) = 100
7(300/8-w -w) = 100
7(300/8-2w) = 100
300/8-2w = 100/7
-2w = 100/7-300/8
multiplying both sides by 56:
-112w = 800-2100
-112w = -1300
w = 11.61 mph

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