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 for the entire trip, they would have arrived 30 minutes s

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 for the entire trip, they would have arrived 30 minutes s      Log On


   

Question 203097: 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 for 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 for the entire trip,
they would have arrived 30 minutes sooner. What was Loren's rate?
:
Let r = Loren's rate
then
(r-10) = Lois' rate
:
Write a time equation: Time = dist%2Frate
:
Convert 30 min to .5 hrs
:
Loren's drive time + Lois drive time = Loren's drive time + 30 min (.5 hr)
200%2Fr + 100%2F%28%28r-10%29%29 = 300%2Fr + .5
multiply equation by: r(r-10), results
200(r-10) + 100r = 300(r-10) + .5r(r-10)
:
200r - 2000 + 100r = 300r - 3000 + .5r^2 - 5r
:
300r - 2000 = 300r - 3000 + .5r^2 - 5r
:
0 = 300r - 300r - 3000 + 2000 .5r^2 - 5r
A quadratic equation
.5r^2 - 5r - 1000 = 0
Multiply by 2 to get rid of the decimal
r^2 - 10r - 2000 = 0
Factor
(r-50)(r+40) = 0
Positive solution
r = 50 mph is Loren's speed
:
:
Check solution in original equation (40 mph is Lois' speed)
200%2F50 + 100%2F40 = 300%2F50 + .5
4 + 2.5 = 6 + .5