Question 1067383: Two workers and B together could finish a work in 8 days. They worked together for 6 days and A left the work. The remaining work was completed by B alone in 6 days. How many days would each take to complete the work individually ?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! What we have to find is
 = number of days that it would take worker A to complete the job by himself (or herself),
and
 = number of days needed for B to complete the job working alone.
In one day of work, the fraction of the job that
A would complete is  ,
and the fraction of the job B would complete
is  .
Working together, they would complete
 of the job each day,
and that would be  of the job.
(You could also say that
 ),
but either way, you end up with
 .
 is the fraction of the job
that A and B complete, working together,
during the first 6 days.
 is the fraction of the whole job
that B does all alone, during the next 6 days.
After that, the fraction of the job that has been completed is
 or  .
We solve that to find :
Multiplying both sides of the equal sign times 
we get the equivalent equation
 .
Now, substituting the value for
into ,
we get  ,
which we solve for .
First, we multiply both sides of the equal sign
times  to get the equivalent equation
 .
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