Question 209730
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/speed}}}
:
time to work - time home = 10 min ({{{1/6}}} hour)
{{{56/((s-8))}}} - {{{56/s}}} = {{{1/6}}}
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 {{{1/6}}} of an hr