SOLUTION: 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?

Question 302721: 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 ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 = the rate of the wind
let s = the flying rate of the hawk
then
(s+w) = effective speed with the wind
(s-w) = effective speed against the wind
:
Two distance equations:
8(s+w) = 300
7(s-w) = 100
:
8s + 8w = 300
7s - 7w = 100
:
Multiply the 1st equation by 7 & the 2nd equation by 8, subtract
56s + 56w = 2100
56s - 56w = 800
-------------------subtraction eliminates s, find w
112w = 1300
w =
w = 11.6 mph is the rate of the wind
:
:
Find the speed of the hawk to check our solution for the wind
8s + 8(11.6) = 300
8s = 92.8 = 300
8s = 300 - 92.8
s =
s = 25.9 mph
:
Check it in the 2nd equation
7s - 7w = 100
7(25.9) - 7(11.6) =
181.3 - 81.2 = 100.1 ~ 100; confirms our solution for wind = 11.6 mph
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