Question 781457
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
{{{2/((s-3))}}} + {{{6/s}}} = 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