SOLUTION: A man rode a bycycle for 12 mi and then hiked an additional 8 mi. The total time for the trip was 5 hr. If his biking was 10 mph faster than his hiking rate, what was each rate?

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Question 458480: A man rode a bycycle for 12 mi and then hiked an additional 8 mi. The total time for the trip was 5 hr. If his biking was 10 mph faster than his hiking rate, what was each rate?
Answer by ankor@dixie-net.com(22740) (Show Source):
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A man rode a bicycle for 12 mi and then hiked an additional 8 mi.
The total time for the trip was 5 hr.
If his biking was 10 mph faster than his hiking rate, what was each rate?
:
Let r = his hiking rate
it says," biking was 10 mph faster than his hiking rate". therefore:
(r+10) = his biking rate
:
Write a time equation, time = dist/speed
:
hike time + bike time = 5 hrs
+ = 5
:
multiply by r(r+10)
r(r+10)*8 + r(r+10)*12 = r(r+10)*5
:
Cancel the denominators and you have:
8(r+10) + 12r = 5r(r+10)
:
8r + 80 + 12r = 5r^2 + 50r
:
20r + 80 = 5r^2 + 50r
Combine on the right
0 = 5r^2 + 50r - 20r - 80
A quadratic equation
5r^2 + 30r - 80 = 0
simplify divide by 5
r^2 + 6r - 16 = 0
factors to
(r+8)(r-2) = 0
the positive solution
r = 2 mph is his hiking speed
then
2 + 10 + 12 mph is his biking speed
:
:
Check this by finding the times
12/12 + 8/2 = 5