SOLUTION: Tina is training for a biathlon. To train for the running portion of the race, she runs 10 miles each day, over the same course. The first 4 miles of the course is on level ground,

Algebra ->  Rational-functions -> SOLUTION: Tina is training for a biathlon. To train for the running portion of the race, she runs 10 miles each day, over the same course. The first 4 miles of the course is on level ground,      Log On


   

Question 423740: Tina is training for a biathlon. To train for the running portion of the race, she runs 10 miles each day, over the same course. The first 4 miles of the course is on level ground, while the last 6 miles is downhill. She runs 4 miles per hour slower on level ground than she runs downhill. If the complete course takes 1 hour, how fast does she run on the downhill part of the course
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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runs 10 miles each day, over the same course.
The first 4 miles of the course is on level ground, while the last 6 miles is downhill.
She runs 4 miles per hour slower on level ground than she runs downhill.
If the complete course takes 1 hour, how fast does she run on the downhill part of the course?
:
Let s = the speed downhill
then
(s-4) = the speed on level ground
:
Write a time equation: Time = dist/speed
:
Downhill time + level time = 1 hr
6%2Fs + 4%2F%28%28s-4%29%29 = 1
Multiply by s(s-4)*
s(s-4)*6%2Fs + s(s-4)*4%2F%28%28s-4%29%29 = s(s-4)*1
Cancel the denominators
6(s-4) + 4s = s^2 - 4s
6s - 24 + 4s = s^2 - 4s
10s - 24 = s^2 - 4s
Combine like terms on the right
0 = s^2 - 4s - 10s + 24
A quadratic equation
s^2 - 14s + 24 = 0
Factors to
(s-2)(s-12) = 0
the reasonable solution
s = 12 mph down hill
:
:
Check this (Level speed = 8)
4/8 + 6/12 = 1