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?
:
Let r = Loren's rate
then
(r-10) = Lois' rate
:
Write a time equation: Time = {{{dist/rate}}}
:
Convert 30 min to .5 hrs
:
Loren's drive time + Lois drive time = Loren's drive time + 30 min (.5 hr)
{{{200/r}}} + {{{100/((r-10))}}} = {{{300/r}}} + .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)
{{{200/50}}} + {{{100/40}}} = {{{300/50}}} + .5
4 + 2.5 = 6 + .5