SOLUTION: A race has two parts, an 18km run and a 30km canoe race. The canoeists travelled 8km/h faster than the runner. The winning time was exactly 3h. How fast did the runner travel?

Question 838449: A race has two parts, an 18km run and a 30km canoe race. The canoeists travelled 8km/h faster than the runner. The winning time was exactly 3h. How fast did the runner travel?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A race has two parts, an 18km run and a 30km canoe race.
The canoeists travelled 8km/h faster than the runner.
The winning time was exactly 3h.
How fast did the runner travel?
:
let r = runner's speed
then
(r+8) = canoe speed
:
Write a time equation; time = dist/speed
run time + canoe time = 3 hrs
+ = 3
mult by r(r+8), cancel the denominators, you have:
18(r+8) + 30r = 3r(r+8)
18r + 144 + 30r = 3r^2 + 24r
48r + 144 = 3r^2 + 24r
Combine as a quadratic equation on the right
0 = 3r^2 + 24r - 48r - 144
0 = 3r^2 - 24r - 144
simplify divide by 3
r^2 - 8r - 48 = 0
Factors to
(r+4)(r-12) = 0
The positive solution
r = 12 km/h is the runners speed
:
:
Check this
+ =
1.5 + 1.5 = 3

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