SOLUTION: Joshua and Geraldine can finish cleaning the house in 2 hours. If it takes Joshua working alone 3 hours longer than it takes Geraldine working alone, how many hours will each need

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Joshua and Geraldine can finish cleaning the house in 2 hours. If it takes Joshua working alone 3 hours longer than it takes Geraldine working alone, how many hours will each need       Log On


   

Question 384665: Joshua and Geraldine can finish cleaning the house in 2 hours. If it takes Joshua working alone 3 hours longer than it takes Geraldine working alone, how many hours will each need to finish the work alone?
Found 2 solutions by mananth, edjones:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Joshua and Geraldine can finish cleaning the house in 2 hours. If it takes Joshua working alone 3 hours longer than it takes Geraldine working alone, how many hours will each need to finish the work alone?
...
Geraldine = xhours
Joshua x+3 hours
they both can do
...
%282x%2B3%29%2F%28x%5E2-3x%29
they will take %28x%5E2-3x%29%2F%282x%2B3%29 to complete the job
..
%28x%5E2-3x%29%2F%282x%2B3%29=2
..
x^2-3x=2(2x+3)
x^2-3x=4x+6
x^2-3x-4x-6=0
x^2-7x-6=0
discriminant = 73
x1=%287%2Bsqrt73%29%2F%282%29
x1=7.77 hours
Geraldine%28highlight%287.77%29%29hours
Joshua%28highlight%2810.77%29%29 hours
..
x2 will be negative so ignore
m.ananth@hotmail.ca

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
1/g amount of the job geraldine can do in 1 hr
1/(g+3) amount of the job josh can do in 1 hr
1/g + 1/(g+3) = 1/2 working togeter to do 1/2 the job.
2(g+3)+2g=g^2+3g multiply each side by 2g(g+3) LCM.
2g+6+2g=g^2+3g
g^2-g-6=0
(g-3)(g+2)=0
g=3 hrs to do the job alone
Josh will 6 hrs to do the job alone
.
Ed