SOLUTION: Loren drove 200 miles at a certain rate and his wife Lois drove 100 miles at a rate 10 mph slower. If loren had driven the entire trip they would have arrived 30 minutes sooner Wha

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Loren drove 200 miles at a certain rate and his wife Lois drove 100 miles at a rate 10 mph slower. If loren had driven the entire trip they would have arrived 30 minutes sooner Wha      Log On


   

Question 139112: Loren drove 200 miles at a certain rate and his wife Lois drove 100 miles at a rate 10 mph slower. If loren had driven the entire trip they would have arrived 30 minutes sooner What was Loren's rate.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Loren drove 200 miles at a certain rate and his wife Lois drove 100 miles at a rate 10 mph slower. If loren had driven the entire trip they would have arrived 30 minutes sooner What was Loren's rate.
:
Let s = Lor rate of speed
then
(s-10) = Loi's rate of speed
:
Write a time equation: Time = dist/speed
:
Lor time + .5 hr = Lor's + Loi's time
300%2Fs + .5 = 200%2Fs + 100%2F%28%28s-10%29%29
Multiply equation by s(s-10) to get rid of the denominators
s(s-10)*300%2Fs + .5s(s-10) = s(s-10)*200%2Fs + s(s-10)*100%2F%28%28s-10%29%29
Cancel out the denominators and you have:
300(s-10) + .5s^2 - 5s = 200(s-10) + 100s
:
300s - 3000 + .5s^2 - 5s = 200s - 2000 + 100s
:
group like terms on the left:
.5s^2 + 300s - 5s - 200s - 100s - 3000 + 2000 = 0
:
.5s^2 - 5s - 1000 = 0
:
Multiply eq by 2, to make the coefficient of s^2 = 1
s^2 - 10s - 2000 = 0
Factor
(s-50)(s+40) = 0
Positive solution:
s = +50 mph is Lore's speed
:
:
Check solution by finding the times:
200/50 + 100/40 = 6.5 hrs
300/50 = 6 hrs