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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=640 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 28.6491106406735, 3.35088935932648. Here's your graph:

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

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