SOLUTION: It takes copy machine A one hour less to complete a copying task when working alone than it takes copy machine B working alone. If both copiers are used, they can complete the task

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Question 902682: It takes copy machine A one hour less to complete a copying task when working alone than it takes copy machine B working alone. If both copiers are used, they can complete the task in 72 minutes. How long does it take each machine to complete the task when working alone?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/a+1/b=1/x
1/a+1/(a+1)=1/72
(a+1+a)/(a*(a+1))
2a+1/(a^2+a)=1/72
72*(2a+1)=a^2+a
144a+72=a^2+a
a^2-143a-72=0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 1a%5E2%2B-143a%2B-72+=+0) has the following solutons:

a%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=%28-143%29%5E2-4%2A1%2A-72=20737.

Discriminant d=20737 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--143%2B-sqrt%28+20737+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%28-143%29%2Bsqrt%28+20737+%29%29%2F2%5C1+=+143.50173609018
a%5B2%5D+=+%28-%28-143%29-sqrt%28+20737+%29%29%2F2%5C1+=+-0.501736090180486

Quadratic expression 1a%5E2%2B-143a%2B-72 can be factored:
1a%5E2%2B-143a%2B-72+=+1%28a-143.50173609018%29%2A%28a--0.501736090180486%29
Again, the answer is: 143.50173609018, -0.501736090180486. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-143%2Ax%2B-72+%29

a=143.50 a+1=144.50