SOLUTION: It takes sasha and miranda 8 hours to clean a house. It would take miranda 12 more hours than sasha to clean the house alone. How long will it take sasha to ckean the house??

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes sasha and miranda 8 hours to clean a house. It would take miranda 12 more hours than sasha to clean the house alone. How long will it take sasha to ckean the house??       Log On


   

Question 738575: It takes sasha and miranda 8 hours to clean a house. It would take miranda 12 more hours than sasha to clean the house alone. How long will it take sasha to ckean the house??

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let sasha take x hours to clean the house. which is 1 job
so she does 1/x of the job in 1 hour
Miranda takes x+12 hours to do the job
so 1/(x+12) of the job is done in 1 hour
1%2Fx+%2B1%2F%28x%2B12%29 of the job they do in 1 hour
+%28%28x%2B12%29%2Bx%29%2F%28x%28x%2B12%29%29+
%282x%2B12%29%2F%28x%28x%2B12%29%29
to complete the job they will take %28x%28x%2B12%29%29%2F%282x%2B12%29hours
%28x%28x%2B12%29%29%2F%282x%2B12%29 = 8
Solve
x%5E2%2B12x=8%282x%2B12%29

x%5E2%2B12x=16x%2B96

rearrange
x%5E2-4x-96=0
x%5E2-12x%2B8x-96=0

x%28x-12%29%2B8%28x-12%29=0
(x-12)(x+8)=0
x=12 OR x=-8
Ignore negative
x= 12 hours --------- sasha's time to complete the job alone