SOLUTION: Cindy can paint a house in 3 hr less time than Dustin. Together, it takes 18 hrs. How long does it take each to do the job by theirselves?

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Question 461620: Cindy can paint a house in 3 hr less time than Dustin. Together, it takes 18 hrs. How long does it take each to do the job by theirselves?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Cindy can paint a house in 3 hr less time than Dustin. Together, it takes 18 hrs. How long does it take each to do the job by theirselves?
.
Let x = time (hrs) it takes for Dustin
then
x-3 = time it takes for Cindy
.
18(1/x + 1/(x-3)) = 1
multiplying both sides by x(x-3):
18((x-3) + x) = x(x-3)
18(2x-3) = x^2-3x
36x-54 = x^2-3x
-54 = x^2-39x
0 = x^2-39x+54
solve by applying the "quadratic formula" to get:
x = {37.56, 1.44}
throw out the 1.44 (extraneous) to get
x = 37.56 hours (Dustin)
.
Cindy
x-3 = 37.56-3 = 34.56 hours
.
Details 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-39x%2B54+=+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=%28-39%29%5E2-4%2A1%2A54=1305.

Discriminant d=1305 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--39%2B-sqrt%28+1305+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-39%29%2Bsqrt%28+1305+%29%29%2F2%5C1+=+37.5623918681884
x%5B2%5D+=+%28-%28-39%29-sqrt%28+1305+%29%29%2F2%5C1+=+1.43760813181156

Quadratic expression 1x%5E2%2B-39x%2B54 can be factored:
1x%5E2%2B-39x%2B54+=+1%28x-37.5623918681884%29%2A%28x-1.43760813181156%29
Again, the answer is: 37.5623918681884, 1.43760813181156. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-39%2Ax%2B54+%29