SOLUTION: Two men, A and B, can paint a house in 8 days. A alone can paint it in 12 days. How long will B take to paint the house by himself. I am unsure on how to solve this. All I know

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Question 120361: Two men, A and B, can paint a house in 8 days. A alone can paint it in 12 days. How long will B take to paint the house by himself.
I am unsure on how to solve this. All I know is that there is some formula to this that involves many proportions. Please help!
Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Two men, A and B, can paint a house in 8 days. A alone can paint it in 12 days. How long will B take to paint the house by himself.
:
Let B = time required by B to paint the house by himself
:
Let the completed job = 1
:
A simple equation:
+ = 1
:
Multiply equation by 12B to get rid of the denominators
12B* + 12B* = 12B(1)
;
Cancel out the denominators and you have:
8B + 12(8) = 12B
:
8B + 96 = 12B
:
96 = 12B - 8B
:
96 = 4B
:
B = 96/4
:
B = 24 days
:
:
Check solution:
+ =
+ = 1; confirms our solution

Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
yes, there is "some formula", but if you look at the problem and understand what's going on, its pretty easy

when multiple people work together on a task, each one does some fraction
__ that fraction is based on how fast a person can do the job alone
__ fraction of task=(time together)/(time alone)

think about it __ if Joe can do a job in 3 hrs, and he works in a group that takes 1 hr, Joe does 1/3 of the job

in 8 days, A does 8/12 or 2/3 of the job
__ this means it takes B 8 days to do 1/3 of the job

so how many days for B to do 3/3 (the whole thing)?