SOLUTION: Trisha ran to the park and then walked home. It took her 1/2 hour to run to the park, and 1 hour and 20 minutes to walk home. If she runs 5 miles an hour faster than she walks, how

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Trisha ran to the park and then walked home. It took her 1/2 hour to run to the park, and 1 hour and 20 minutes to walk home. If she runs 5 miles an hour faster than she walks, how      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 168236: Trisha ran to the park and then walked home. It took her 1/2 hour to run to the park, and 1 hour and 20 minutes to walk home. If she runs 5 miles an hour faster than she walks, how far does she live from the park?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Running:
d%5Br%5D+=+r%5Br%5D%2At%5Br%5D
Walking:
d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
Given:
t%5Br%5D+=+1%2F2hrs
t%5Bw%5D+=+4%2F3hrs
r%5Br%5D+=+r%5Bw%5D+%2B+5 mi/hr
Putting this data back into the equations:
d%5Br%5D+=+%28r%5Bw%5D+%2B+5%29%2A%281%2F2%29
d%5Bw%5D+=+r%5Bw%5D%2A%284%2F3%29
From the problem, I know d%5Br%5D+=+d%5Bw%5D, so
%28r%5Bw%5D+%2B+5%29%2A%281%2F2%29+=+r%5Bw%5D%2A%284%2F3%29
multiply both sides by 6
3r%5Bw%5D+%2B+15+=+8r%5Bw%5D
5r%5Bw%5D+=+15
r%5Bw%5D+=+3
And, since
r%5Br%5D+=+r%5Bw%5D+%2B+5
r%5Br%5D+=+3+%2B+5
r%5Br%5D+=+8
And
d%5Br%5D+=+r%5Br%5D%2A%281%2F2%29
d%5Br%5D+=+8%2A%281%2F2%29
d%5Br%5D+=+4
d%5Bw%5D+=+r%5Bw%5D%2A%284%2F3%29
d%5Bw%5D+=+3%2A%284%2F3%29
d%5Bw%5D+=+4
This verifies that
d%5Br%5D+=+d%5Bw%5D+=+4mi answer