SOLUTION: Here is one word problem: You commute 56 miles one way to work.The trip to work takes 10 minutes longer than the trip home. Your average speed on the trip home is 8 miles per hou

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Here is one word problem: You commute 56 miles one way to work.The trip to work takes 10 minutes longer than the trip home. Your average speed on the trip home is 8 miles per hou      Log On


   

Question 209730: Here is one word problem:
You commute 56 miles one way to work.The trip to work takes 10 minutes longer than the trip home. Your average speed on the trip home is 8 miles per hour faster. What is your average speed on the trip home?
Thanks a tone!
Jenn
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You commute 56 miles one way to work.
The trip to work takes 10 minutes longer than the trip home.
Your average speed on the trip home is 8 miles per hour faster.
What is your average speed on the trip home?
:
Let s = speed home
then
(s-8) = speed to work
:
Write a time equation: Time = dist%2Fspeed
:
time to work - time home = 10 min (1%2F6 hour)
56%2F%28%28s-8%29%29 - 56%2Fs = 1%2F6
Multiply equation by s(s-8), results
6s(56) - 6(s-8)*56 = s(s-8)
:
336s - 56(6s-48) = s^2 - 8s
:
336s - 336s + 2688 = s^2 - 8s
A quadratic equation:
s^2 - 8s - 2688 = 0
Factors to:
(s-56)(s+48) = 0
Positive solution:
s = 56 mph, speed home from work
:
:
Check solution (speed to work = 48 mph)
56/48 - 56/56 =
1.667 - 1.0 = .667 hr difference which is 1%2F6 of an hr