SOLUTION: An athlete runs 10 miles and then walks home. The trip home takes 1 hour longer than it took to run that distance. If the athlete runs 5 miles per hour faster than she walks, what

Question 498157: An athlete runs 10 miles and then walks home. The trip home takes 1 hour longer than it took to run that distance. If the athlete runs 5 miles per hour faster than she walks, what are her average running and walking speeds?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An athlete runs 10 miles and then walks home.
The trip home takes 1 hour longer than it took to run that distance.
If the athlete runs 5 miles per hour faster than he walks, what are his average running and walking speeds?
:
let s = his walking speed
then
(s+5) = his running speed
:
Write a time equation; time = dist/speed
:
Run speed = Walk speed + 1 hr
= + 1
:
multiply by s(s+5), results
10s = 10(s+5) + s(s+5)
:
10s = 10s + 50 + s^2 + 5s
combine this as a quadratic equation
s^2 + 5s - 50 = 0
Factors to:
(s+10)(s-5) = 0
positive solution
s = 5 mph is his walking speed
then, obviously, 10 mph is his running speed
:
:
confirm this. find the actual times
10/5 = 2hr
10/10= 1hr
-------------
diff: 1 hr

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