SOLUTION: If Norm and cliff together can paint a room in 4 hours, and Norm can paint the same room in 3 hours less than cliff, How long does it take cliff to paint the room by himself?

Question 249507: If Norm and cliff together can paint a room in 4 hours, and Norm can paint the same room in 3 hours less than cliff, How long does it take cliff to paint the room by himself?
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let c=time it takes cliff to paint a room. Let n=time it takes norm.
n=c-3
Cliff can do 1/c of the job in 1 hr
Norm can do 1/(c-3) of the job in 1 hour
together they can do 1/4 the job in 1 hr.
1/(c-3) + 1/c = 1/4
4c+4(c-3)=c(c-3) multiply each side by 4c(c-3) to eliminate fractions.
4c+4c-12=c^2-3c
c^2-11c+12=0
c=9.77 hrs
.
Ed
.

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=73 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.77200187265877, 1.22799812734123. Here's your graph:

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