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

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) (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 =
:
Convert 30 min to .5 hrs
:
Loren's drive time + Lois drive time = Loren's drive time + 30 min (.5 hr)
+ = + .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)
+ = + .5
4 + 2.5 = 6 + .5

RELATED QUESTIONS
Loren drove 200 miles at a certain rate and his wife Lois drove 100 miles at a rate 10... (answered by ankor@dixie-net.com)

Loren drove 200 miles at a certain rate, and his wife lois drove 100 miles at a rate 10... (answered by Theo)

Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 (answered by richwmiller)

A man drove a certain distance at a uniform rate. If his rate had been 3 miles per hour... (answered by josgarithmetic)

Xavier drove 100 miles at a rate of 60 miles per hour and then he drove another 100 miles (answered by Alan3354)

I'm really in need of help! Mike drove for 3 hours at a certain rate and for 4 hours at... (answered by Alan3354)

Stanley drove 240 miles at a certain rate of speed. If he had traveled 15 mph faster, he... (answered by ankor@dixie-net.com)

A man drove 156 miles at a constant rate. If he had driven 5 miles per hour faster he... (answered by stanbon)

Jeremy drove 54 miles in 45 minutes. If he drove at a constant rate, what is his speed in (answered by TimothyLamb)