SOLUTION: Felipe jogs for 12 miles and then walks another 12 miles. He jogs miles 2 per hour faster than he walks, and the entire distance of 24 miles takes 9 hours. Find the rate at which h

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Question 761493: Felipe jogs for 12 miles and then walks another 12 miles. He jogs miles 2 per hour faster than he walks, and the entire distance of 24 miles takes 9 hours. Find the rate at which he walks and the rate at which he jogs.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Felipe jogs for 12 miles and then walks another 12 miles.
He jogs miles 2 per hour faster than he walks, and the entire
distance of 24 miles takes 9 hours.
Find the rate at which he walks and the rate at which he jogs.
:
Let w = his walking speed
then
(w+2) = his jogging speed
:
Write a time equation: time = dist/speed
:
Jog time + walk time = 9 hrs
12%2F%28%28w%2B2%29%29 + 12%2Fw = 9
multiply by w(w+2), cancel the denominators and you have:
12w + 12(w+2) = 9w(w+2)
12w + 12w + 24 = 9w^2 + 18w
Arrange as a quadratic equation on the right:
0 = 9w^2 + 18w - 24w - 24
9w^2 - 6w - 24 = 0
simplify divide by 3
3w^2 - 2w - 8 = 0
Factors to
(2w+4)(w-2) = 0
the positive solution is all we want here
w = 2 mph is his walking speed
then, obviously:
4 mph is the jogging speed
:
:
Check this out by finding the times
12/2 = 6 hr
12/4 = 3 hrs
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tot time: 9 hrs