SOLUTION: Two workers A 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 day

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Question 1067736: Two workers A 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?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Rate for A AND B, 1%2Fx%2B1%2Fy=1%2F8

Rate for just B, 1%2Fy

ONE JOB to be done:

%281%2Fx%2B1%2Fy%29%2A6%2B%281%2Fy%296=1

%281%2F8%29%2A6%2B%281%2Fy%296=1
3%2F4%2B6%2Fy=1
Common Denominator, 4y.

4y%283%2F4%29%2B4y%286%2Fy%29=4y

3y%2B24=4y

24=y-----------Worker B would need 24 days to do all the 1 job alone.



Now find x, the time for worker A to do the 1 job alone.

Answer by ikleyn(52779) About Me  (Show Source):
You can put this solution on YOUR website!
.
Two workers A 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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Since two workers A and B together could finish the work in 8 days, and since they worked together for 6 days, 
they just completed 6%2F8 = 3%2F4 of the work.

Hence, the remaining is 1%2F4 of the work.

Since B completes it (completes this 1%2F4 of the work) in 6 days, he can make the entire job in 6*4 = 24 days.


Now, the condition says that they complete the job in 8 days, working together.
During these 8 days, worker B makes 1%2F3 of the job.

Hence, worker A alone makes 2%2F3 of the job in 8 days.

Then, A makes the entire job in 12 days.

Solved. A needs 12 days to complete the job alone.
             B needs 24 days to complete the job alone..


You do not need solve equations to get the answer.
All you need is to organize your thoughts LOGICALLY.


There is a wide variety of solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work,
    - Solving more complicated word problems on joint work,
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".