SOLUTION: Alan takes 6 days less than Bob to finisha task at work. If both Alan and Bob worktogether, they can finish the work in 4 days. Findthe time that Bob would take to finish the workb

Algebra ->  Finance -> SOLUTION: Alan takes 6 days less than Bob to finisha task at work. If both Alan and Bob worktogether, they can finish the work in 4 days. Findthe time that Bob would take to finish the workb      Log On


   

Question 1180674: Alan takes 6 days less than Bob to finisha task at work. If both Alan and Bob worktogether, they can finish the work in 4 days. Findthe time that Bob would take to finish the workby himself.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

Alan takes 6 days less than Bob to finish task at work.
let Bob take x days to finish the job alone
Bob does 1/x of thejob in 1 day
alan does 1/(x-6) of the job in 1 day
Alan will take x-6 days to finish the job alone
both Alan and Bob work together, they can finish the work in 4 days
Together they do 1/4 of the job in 1 day
1/x + 1/(x-6) = 1/4
Multiply the terms by x(x-6)*4
4(x-6) +4x = x(x-6)
4x-24 +4x= x^2-6x
x^2-14x+24=0
(x-12)(x-2)=0
x=12 OR 2
2 is not possible
Bob takes 12 days alone