SOLUTION: This weekend, while my fiance and daughter were out of town, I decided to paint my living room. I am a horrible painter, but my mom Mary, is excellent. It takes me 4 more hours t

Question 206336: This weekend, while my fiance and daughter were out of town, I decided to paint my living room. I am a horrible painter, but my mom Mary, is excellent. It takes me 4 more hours to paint room the same size of my living room than it takes my mom. We painted the room in 5 hours together. If we worked independently, how long would it take to finish painting the room?

Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
It takes me 4 more hours to paint room the same size of my living room than it takes my mom. We painted the room in 5 hours together. If we worked independently, how long would it take to finish painting the room?
--------------
It takes your mom x hours to paint the room.
It takes you x + 4 hours.
---------------------
Your mom does 1/x of the job per hour.
You do 1/(x+4) per hour.
Together, you do 1/x + 1/(x+4)
1/x + 1/(x+4) = ((x+4) + x)/x(x+4)
That's the part of the job you do together per hour.
Hours/job is the inverse
= x(x+4)/(2x+4) = 5 hours
x^2+4x = 10x+20
x^2 - 6x - 20 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=116 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8.3851648071345, -2.3851648071345. Here's your graph:

-------------
Ignore the negative answer.
x = 3+ sqrt(29) hours for your mom
x+4 = 7 + sqrt(29) for you

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It takes me 4 more hours to paint room the same size of my living room than it takes my mom.
We painted the room in 5 hours together.
If we worked independently, how long would it take to finish painting the room?
:
Let t = time required by mom
then
(t+4) = time required by me
;
Let the completed job = 1
:
+ = 1
:
Multiply equation by t(t+4), results
5(t+4) + 5t = t(t+4)
:
5t + 20 + 5t = t^2 + 4t
:
Arrange as a quadratic on the right:
0 = t^2 + 4t - 10t - 20
:
t^2 - 6t - 20 = 0
:
Use the quadratic equation to find t
:

in the problem:
x=t: a=1; b=-6; c=-20

the positive solution

t =
t = 8.385 hr is Mom's time alone
then
8.385 + 4 = 12.385 is my time alone
:
:
Check solution:
+ =
.596 + .404 = 1
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