SOLUTION: One machine works 8 hours faster then a second machine. If the two machines take twelve hours to finish the job working together, how long will it take them individually. I just

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Question 446552: One machine works 8 hours faster then a second machine. If the two machines take twelve hours to finish the job working together, how long will it take them individually.
I just need to figure out how to get to aquadratic equasion.
Found 2 solutions by nerdybill, Alan3354:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
One machine works 8 hours faster then a second machine. If the two machines take twelve hours to finish the job working together, how long will it take them individually.
.
Let x = time (hrs) it takes for slower machine
then
x-8 = time of faster machine
.
12(1/x + 1/(x-8)) = 1
multiplying both sides by x(x-8):
12(x-8 + x) = x(x-8)
12(2x-8) = x(x-8)
24x-96 = x^2-8x
-96 = x^2-32x
0 = x^2-32x+96
applying the quadratic equation we get:
x = {28.65, 3.35}
we can throw out the 3.35 leaving:
x = 28.65 hrs (slower machine)
.
faster machine:
x-8 = 28.65-8 = 20.65 hrs
.
detail of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-32x%2B96+=+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=%28-32%29%5E2-4%2A1%2A96=640.

Discriminant d=640 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--32%2B-sqrt%28+640+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-32%29%2Bsqrt%28+640+%29%29%2F2%5C1+=+28.6491106406735
x%5B2%5D+=+%28-%28-32%29-sqrt%28+640+%29%29%2F2%5C1+=+3.35088935932648

Quadratic expression 1x%5E2%2B-32x%2B96 can be factored:
1x%5E2%2B-32x%2B96+=+1%28x-28.6491106406735%29%2A%28x-3.35088935932648%29
Again, the answer is: 28.6491106406735, 3.35088935932648. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-32%2Ax%2B96+%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
"8 hours faster" does not make sense.