SOLUTION: Imogene's car traveled 336 miles averaging a certain speed. If the car had gone 6 mph faster, the trip would have takes 1 hour less. Find the average speed.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Imogene's car traveled 336 miles averaging a certain speed. If the car had gone 6 mph faster, the trip would have takes 1 hour less. Find the average speed.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 904050: Imogene's car traveled 336 miles averaging a certain speed. If the car had gone 6 mph faster, the trip would have takes 1 hour less. Find the average speed.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
336mi%2Fr+-+336%2F%28r%2B6%29+=+1 |Multiplying thru by r(r+6) so as all denominators = 1
336(r+7) - 336r = r(r+6)
r^2 + 6r - 2352 = 0 (Tossing out the negative solution for unit measure)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-2352+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A-2352=9444.

Discriminant d=9444 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+9444+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+9444+%29%29%2F2%5C1+=+45.5901224530254
x%5B2%5D+=+%28-%286%29-sqrt%28+9444+%29%29%2F2%5C1+=+-51.5901224530254

Quadratic expression 1x%5E2%2B6x%2B-2352 can be factored:
1x%5E2%2B6x%2B-2352+=+1%28x-45.5901224530254%29%2A%28x--51.5901224530254%29
Again, the answer is: 45.5901224530254, -51.5901224530254. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-2352+%29