SOLUTION: Two cars travel at uniform rates of speed over the same route a distance of 180 ml. One goes 5 mph slower than the other and takes 1/2 hr longer to make the run. How fast does each

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Two cars travel at uniform rates of speed over the same route a distance of 180 ml. One goes 5 mph slower than the other and takes 1/2 hr longer to make the run. How fast does each      Log On


   

Question 814815: Two cars travel at uniform rates of speed over the same route a distance of 180 ml. One goes 5 mph slower than the other and takes 1/2 hr longer to make the run. How fast does each car travel?
I JUST CANT PLOT THE EQUATIONS TO SOLVE THIS QUADRATIC PROBLEM.PLEASE, HELP.
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two cars travel at uniform rates of speed over the same route a distance of 180 ml.
One goes 5 mph slower than the other and takes 1/2 hr longer to make the run.
How fast does each car travel?
:
Let s = the speed of car A
then
(s+5) = the speed of car B
:
Write a time equation, time = dist/speed
:
A car's time - B car's time = .5 hrs
180%2Fs - 180%2F%28%28s%2B5%29%29 = .5
mult equation by s(s+5), cancelling the denominators, you have
180(s+5) - 180s = .5s(s+5)
180s + 900 - 180s = .5s^2 + 2.5s
Combine on the right as a quadratic equation
0 = .5s^2 + 2.6s - 900
multiply by 2, get rid of the decimals
s^2 + 5s - 1800 = 0
Factors to
(s+45)(s-40) = 0
the positive solution is what we want here
s = 40 mph for car A
and,obvously:
45 mph for Car B
:
:
Check this out, find the time for each car
180/40 = 4.5 hrs
180/45 = 4.0 hrs, a half hr difference

Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Try to make a data table.

Let r = speed of the other car.

CAR_______________speed_____________time_____________distance
Car_______________r-5_______________(____)___________180
Other car_________r_________________(____)___________180

That much ignores the "takes 1/2 hr longer" part of the description. Let's start filling in time information using r*t=d basic idea.

CAR_______________speed_____________time_____________distance
Car_______________r-5_______________(180%2F%28r-5%29)___________180
Other car_________r_________________(180%2Fr)___________180

Now, about that "one.... takes 1/2 hour longer..."

CAR_______________speed_____________time_____________distance
Car_______________r-5_______________highlight%28180%2F%28r-5%29=1%2F2%2B180%2Fr%29___________180
Other car_________r_________________(180%2Fr)___________180


There you find the equation to solve for r. You might expect it to take the form of a quadratic equation in r as the variable. Say if you have further difficulty with this problem.


NOW INCLUDING FINISH OF SOLUTION: Multiplying both sides by 2r(r-5) and simplifying gives r%5E2-5r-1800=0
Using general solution to quadratic equation gives
.
r=%285%2Bsqrt%2825%2B4%2A1800%29%29%2F2
r=%285%2Bsqrt%2825%2B7200%29%29%2F2
r=%285%2Bsqrt%287225%29%29%2F2
r=%285%2B17%2A5%29%2F2
r=45 for "other car", so "car" goes at 40 mph----------final answers