SOLUTION: A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour fas

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Question 452380: A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip
was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate
walking, what was each rate?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A man rode a bicycle for 12 miles and then hiked an additional 8 miles.
The total time for the trip was 5 hours.
If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?
:
Let s = his walking rate
then
(s+10) = his biking rate
:
Write a time equation; time = dist/speed
:
walk time + biking time = 5 hrs
8%2Fs + 12%2F%28%28s%2B10%29%29 = 5
:
Multiply by s(s+10)
8(s+10) + 12s = 5s(s+10)
8s + 80 + 12s = 5s^2 + 50s
20s + 80 = 5s^2 + 50s
0 = 5s^2 + 50s - 20s - 80
:
A quadratic equation
5s^2 + 30s - 80 = 0
:
Simplify, divide by 5
s^2 + 6s - 16 = 0
:
factors to
(s+8)(s-2) = 0
:
the positive solution is all we want here
s = 2 mph walking speed
then, obviously:
12 mph biking speed
;
:
Check that in the time equation
8%2F2 + 12%2F12 = 5 hrs