SOLUTION: It's 56 miles to work, it takes 10 minutes longer to get to work than coming home, and you travel 8 mph faster coming home. What is your avg. speed coming home?

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Question 214124: It's 56 miles to work, it takes 10 minutes longer to get to work than coming home, and you travel 8 mph faster coming home. What is your avg. speed coming home?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It's 56 miles to work, it takes 10 minutes longer to get to work than coming home,
and you travel 8 mph faster coming home.
What is your avg. speed coming home?
:
Let s = speed coming home
then
(s-8) = speed going to work
:
Convert 10 min to 1%2F6 hr
:
Write a time equation: Time = dist/speed
:
Time from work + 10 min = time to work
56%2Fs + 1%2F6 = 56%2F%28%28s-8%29%29
Multiply equation by 6s(s-8), results:
56*6*(s-8) + s(s-8) = 6s*56
;
336(s-8) + s^2 - 8s = 336s
:
336s - 2688 + s^2 - 8s - 336s = 0
:
Arrange as a quadratic equation
s^2 - 8s - 2688 = 0
Factor to
(s-56)(s+48) = 0
positive solution
s = 56 mph on the return home
:
:
Check solution (speed to work = 48 mph)
56/56 + 1/6 = 56/48
1 + .167 = 1.167