SOLUTION: The Word Problem: Tina is training for a biathlon. To train for the running portion of the race, she runs 8 miles each day over the same course. The first 2 miles of the cours

Question 781457: The Word Problem:
Tina is training for a biathlon. To train for the running portion of the race, she runs 8 miles each day over the same course. The first 2 miles of the course is on level ground, while the last 6 miles is downhill. She runs 3 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?
My Trouble:
I've tried this problem and came to the solution 5.5 MPH downhill using the equation: . However I have been told this is not the correct answer. I know my math is solid on my equation, thus I must have the wrong equation. My thinking behind using this equation was that because her speed downhill is unknown it must be represented by a variable, and her speed on flat ground is 3 less then her speed downhill and so by adding the two we have her total speed over the whole course. I feel as though I'm missing something but I can't figure out exactly what.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
To train for the running portion of the race, she runs 8 miles each day over the same course.
The first 2 miles of the course is on level ground, while the last 6 miles is downhill.
She runs 3 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 = speed downhill
then
(s-3) = speed on level ground
:
Write a time equation.time = dist/speed
level time + downhill time = 1 hr
+ = 1
multiply by s(s-3), resulting in
2s + 6(s-3) = s(s-3)
2s + 6s - 18 = s^2 - 3s
Arrange as a quadratic equation on the right
0 = s^2 - 3s - 8s + 18
s^2 - 11s + 18 = 0
factors to
(s-2)(s-9) = 0
s = 9 mph is the reasonable solution here
:
:
See if that works find the time of each
2/6 + 6/9 = 1
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