SOLUTION: Carmen recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 5 miles per hour faster than on her way home. If Carmen spent

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Question 998631: Carmen recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 5 miles per hour faster than on her way home. If Carmen spent a total of 2 hours bicycling, find the two rates.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Carmen recently rode her bicycle to visit her friend who lives 12 miles away.
On her way there, her average speed was 5 miles per hour faster than on her way home.
If Carmen spent a total of 2 hours bicycling, find the two rates.
:
let s = speed on the way home
then
(s+5) = speed on the way there
:
Write a time equation; time = dist/speed
time there + return time = 2 hrs
12%2F%28%28s%2B5%29%29 + 12%2Fs = 2
multiply equation by s(s+5), cancel the denominators and you have
12s + 12(s+5) = 2s(s+5)
12s + 12s + 60 = 2x^2 + 10s
24s + 60 = 2s^2 + 10s
arrange as a quadratic equation on the right
0 = 2s^2 + 10s - 24s - 60
2s^2 - 14s -60 = 0
simplify, divide by 2
s^2 - 7s - 30 = 0
Factors to
(s-10)(s+3) = 0
the positive solution is all we want here
s = 10 mph her return speed
then obviously,
15 mph is the to speed
:
:
See if that checks out, find the actual time each way
12/15 = .8 hrs
12/10 = 1.2 hrs
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total time: 2 hrs