SOLUTION: Felipe jobs for 10 miles and then walks another 10 miles. He jobs 2 1/2 miles per hour faster than he walks, and the entire distance of 20 miles takes 6 hours. find the rate at w

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Felipe jobs for 10 miles and then walks another 10 miles. He jobs 2 1/2 miles per hour faster than he walks, and the entire distance of 20 miles takes 6 hours. find the rate at w      Log On


   



Question 187282This question is from textbook
: Felipe jobs for 10 miles and then walks another 10 miles. He jobs 2 1/2 miles per hour faster than he walks, and the entire distance of 20 miles takes 6 hours. find the rate at which he walks and the rate at which he jogs. This question is from textbook

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Jogging:
d%5Bj%5D+=+r%5Bj%5D+%2A+t%5Bj%5D
Walking:
d%5Bw%5D+=+r%5Bw%5D+%2A+t%5Bw%5D
given:
d%5Bj%5D+=+10 mi
d%5Bw%5D+=+10 mi
r%5Bj%5D+=+r%5Bw%5D+%2B+2.5 mi/hr
t%5Bj%5D+%2B+t%5Bw%5D+=+6 hr
t%5Bj%5D+=+6+-+t%5Bw%5D hr
--------------------------
Jogging:
10+=+%28r%5Bw%5D+%2B+2.5%29%2A+%286+-+t%5Bw%5D%29
10+=+6r%5Bw%5D+%2B+15+-+r%5Bw%5D%2At%5Bw%5D+-+2.5t%5Bw%5D
10+=+6r%5Bw%5D+%2B+15+-+10+-+2.5t%5Bw%5D
(1)5+=+6r%5Bw%5D+-+2.5t%5Bw%5D
Walking:
10+=+r%5Bw%5D%2At%5Bw%5D
t%5Bw%5D+=+10%2Fr%5Bw%5D
Substitute this in (1)
(1) 5+=+6r%5Bw%5D+-+2.5%2A%2810%2Fr%5Bw%5D%29
multiply both sides by r%5Bw%5D
(1) 5r%5Bw%5D+=+6%2A%28r%5Bw%5D%29%5E2+-+25
(1) 6%2A%28r%5Bw%5D%29%5E2+-+5r%5Bw%5D+-+25+=+0
Use quadratic formula to solve for r%5Bw%5D
Then find t%5Bw%5D, then find r%5Bj%5D