SOLUTION: Set up an equation and solve the following problem. Felipe jogs for 21 miles and then walks another 21 miles. He jogs 3and 1/2 miles per hour faster than he walks, and the enti

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Set up an equation and solve the following problem. Felipe jogs for 21 miles and then walks another 21 miles. He jogs 3and 1/2 miles per hour faster than he walks, and the enti      Log On

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Question 632869: Set up an equation and solve the following problem.
Felipe jogs for 21 miles and then walks another 21 miles. He jogs
3and 1/2 miles per hour faster than he walks, and the entire distance of 42 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):
You can put this solution on YOUR website!
Set up an equation and solve the following problem.
Felipe jogs for 21 miles and then walks another 21 miles.
He jogs 3 and 1/2 miles per hour faster than he walks, and the entire
distance of 42 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+3.5) = his jogging speed
:
Write a time equation, time = dist/speed
:
Walking time + jogging time = 9 hrs
21%2Fw + 21%2F%28%28w%2B3.5%29%29 = 9
multiply by w(w+3.5) to clear the denominators, results:
21(w+3.5) + 21w = 9w(w+3.5)
21w + 73.5 + 21w = 9w^2 + 31.5w
42w + 73.5 = 9w^2 + 31.5w
Arrange as a quadratic equation
0 = 9w^2 + 31.5w - 42w - 73.5
9w^2 - 10.5w - 73.5 = 0
You can use the quadratic formula but this will factor to
(9w+21)(w-3.5) = 0
the positive solution
w = 3.5 mph is his walking speed
then
3.5+3.5 = 7 mph is his jogging speed
:
:
Let's see if that checks out, find the time of each, walking & jogging
21/7 = 3 hr
21/3.5= 6 hr
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tot time: 9 hrs