Question 423740
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/s}}} + {{{4/((s-4))}}} = 1
Multiply by s(s-4)*
s(s-4)*{{{6/s}}} + s(s-4)*{{{4/((s-4))}}} = 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