SOLUTION: Felipe jogs for 10 miles and then walks another 10 miles. He jogs 1.5 miles per hour faster than he walks, and the entire distance of 20 miles takes 6.5 hours. Find the rate at whi

Algebra ->  College  -> Linear Algebra -> SOLUTION: Felipe jogs for 10 miles and then walks another 10 miles. He jogs 1.5 miles per hour faster than he walks, and the entire distance of 20 miles takes 6.5 hours. Find the rate at whi      Log On


   

Question 734240: Felipe jogs for 10 miles and then walks another 10 miles. He jogs 1.5 miles per hour faster than he walks, and the entire distance of 20 miles takes 6.5 hours. Find the rate at which he walks and the rate at which he jogs.
I have no idea how to do this!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Felipe jogs for 10 miles and then walks another 10 miles.
He jogs 1.5 miles per hour faster than he walks, and the entire distance of 20 miles takes 6.5 hours.
Find the rate at which he walks and the rate at which he jogs.
:
Let w = his walking rate
then
(w+1.5) = his jogging rate
:
Write a time equation: time = dist/speed
:
walking time + jogging time = total time
10%2Fw + 10%2F%28%28w%2B1.5%29%29 = 6.5
multiply equation by w(w+1.5) to get rid of the denominators
10(w+1.5) + 10w = 6.5w(w+1.5)
10w + 15 + 10w = 6.5w^2 + 9.75w
combine as a quadratic equation on the right
0 = 6.5w^2 + 9.75w - 20w - 15
6.5w^2 - 10.25w - 15 = 0
You will have to use the quadratic formula to find w
I got a positive solution of 2.5 mph for walking, I have to go right now so I am leaving you with this.