SOLUTION: A water tank has two drainpipes attached to it. The larger pipe can drain the tank in 2 hours less than the smaller pipe. If both pipes are being used, they can drain the tank in 4

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Question 435759: A water tank has two drainpipes attached to it. The larger pipe can drain the tank in 2 hours less than the smaller pipe. If both pipes are being used, they can drain the tank in 4 hours. How long would it takw the smaller pipe to drain the tank working alone?
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
1/t+1/t-2=1/4
4(t-2)+4t=t(t-2)
4t-8+4t=t2-2t
t2-10t+8=0
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

Ignoring the 0 answer, we get t=9.12311
hours and t-2 to be 7.12311 hours..