SOLUTION: 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

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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