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A and B can do a piece of work in 18 and 12 days respectively. they begin together, but B leaves 3 days before the completion of the work. In how many days is the work finished?

2006-09-24 16:46:06 · 6 answers · asked by wud_luv2know 1 in Science & Mathematics Mathematics

6 answers

First, you have to consider how much each person can finish in one day. In this case ..

A completes 1/18th of the job in a day.
B completes 1/12th of the job in a day.

If they are working together, that means that you would add the two amounts together to find out how much is complete in one day.

1/18 = 2/36 and 1/12 = 3/36 (need like denominators).

So together, A and B can complete 5/36ths of the job in a day.

Now ... they go along until they are 3 days from completing the job ...

Day 1 - 5/36 done
Day 2 - 10/36 done
Day 3 - 15/36 done
Day 4 - 20/36 done
Day 5 - 25/36 done
Day 6 - 30/36 done
Day 7 - 35/36 done
And during day 8, they would complete the job working side by side.

BUT!!! B left with 3 days to go ...
So at the start of day 6, they were 25/36 done when A is now working alone -- at a rate of 2/36 per day ..

so with 11/36 left to go and A working alone at 2/36 done per day ... that means it will be another 6 days before the job is done!!

2006-09-24 17:03:23 · answer #1 · answered by TripleFull 3 · 0 0

Well... the question is ambigious. Logically it shall be 18 days because the bottle neck is A not B. Eventhough B is onleave for 3 days, at end of the day, B only using 15 days. Somehow, A still have to have 18 days to do the work. It is like the Racing story of Rabbit and tortoise.

Here are the arguement of your questions if 18 days is not the correct answer.
1. Can B help to do A job once B finished his job?
2. Is it the piece of work is the exactly same work as imply? Meaning, is A and B working on the same job?? or same product with require to Build 2 Products?
3. When B on leaves, can A manage to do B Job?
so on..

2006-09-24 18:11:58 · answer #2 · answered by Mr. Logic 3 · 0 1

the last 3 days, only A worked. work completed = 1/18 X 3 = 1/6

the work done prior to the last 3 days = 1 - 1/6 = 5/6

days worked = (5/6)/(1/18 + 1/12) = 5/6 X (12X18)/12+18 = 6

total = 6 + 3 = 9 days

2006-09-24 17:08:06 · answer #3 · answered by Anonymous · 0 1

The last three days, A works alone. He is doing one sixth of the work in that time. If he had worked along all the time, the remaining work would cost him another 15 days.

Since B works 1 1/2 times as fast as A, together they work 2 1/2 times as fast as A would do alone. Therefore, instead of doing the remaining work in 15 days, they finish it in 2/5th of that time, that is, 6 days.

The total time needed is therefore: 6 days together + 3 days A alone = 9 days in total.

2006-09-24 17:42:09 · answer #4 · answered by dutch_prof 4 · 0 1

A's work rate is 1/18
B's work rate is 1/2
in days they work together the work rate is 1/18+1/12=2/36+3/36=5/36
A has to work alone for 3 days because B left, so he does 3/18,or 6/36 of the job alone
All of the job is 36/36.
36/36-6/36=30/36 of the job was done by them working together.
(30/36)/(5/36)=30/5=6days
it took 6+3=9 days to finish the job.

2006-09-24 17:20:33 · answer #5 · answered by Helmut 7 · 0 1

Figure out what fraction of the work is completed after three days. Subtract from 1 to get the fraction of the work not yet done. Multiply that by 18.

2006-09-24 16:52:03 · answer #6 · answered by Anonymous · 0 1

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