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?

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) (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 (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=1305 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 37.5623918681884, 1.43760813181156. Here's your graph:

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