SOLUTION: Tom and Jerry can paint a room together in 4 hours. Working alone, Tom can paint the room in 2 hours less time than Jerry can. Find how long it takes Jerry to paint the room.

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Question 291479: Tom and Jerry can paint a room together in 4 hours. Working alone, Tom can paint the room in 2 hours less time than Jerry can. Find how long it takes Jerry to paint the room.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let j=number of hrs it takes jerry to do the job.
in one hr jerry can do 1/j of the job and and tom can do 1/(j-2)
1/j + 1/(j-2)=1/4 in one hour
4(j-2)+4j=j(j-2)
4j-8+4j=j^2-2j
j^2-10j+8=0 see below
j=9.12... hrs
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-10x%2B8+=+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=%28-10%29%5E2-4%2A1%2A8=68.

Discriminant d=68 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+68+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+9.12310562561766
x%5B2%5D+=+%28-%28-10%29-sqrt%28+68+%29%29%2F2%5C1+=+0.876894374382339

Quadratic expression 1x%5E2%2B-10x%2B8 can be factored:
1x%5E2%2B-10x%2B8+=+1%28x-9.12310562561766%29%2A%28x-0.876894374382339%29
Again, the answer is: 9.12310562561766, 0.876894374382339. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B8+%29