Question

two workers,if they were workin together, could finish a certain job in 12 days. If one of the workers does the firts half of the job and then the other one does the second half, the job will take them 24 days. How long would it take each worker to do the entire job by himself?

Answer 1

Both workers will take 24 days each to complete the job alone.

Explanation:

Let x A represent number of days taken by 1st worker and B represent number of days taken by 2nd worker.

Part of work completed by worker A in one day
`(1)/(A)`.

Part of work completed by worker B in one day
`(1)/(B)`.

We have been given that two workers ,if they were working together, could finish a certain job in 12 days. We can represent this information in an equation as:

`(1)/(A)+(1)/(B)=(1)/(12)...(1)`

`(B)/(AB)+(A)/(AB)=(1)/(12)...(1)`

`(B+A)/(AB)=(1)/(12)...(1)`

`A+B=(1)/(12)AB...(1)`

We are also told that one of the workers does the first half of the job and then the other one does the second half, the job will take them 24 days. We can represent this information in an equation as:

`(A)/(2)+(B)/(2)=24...(2)`

`(A+B)/(2)=24...(2)`

`A+B=48...(2)`

`A=48-B...(2)`

Upon substituting equation (2) in equation (1), we will get:

`48-B+B=(1)/(12)(48-B)B`

`48=(1)/(12)(48B-B^2)`

`48*12=12*(1)/(12)(48B-B^2)`

`576=48B-B^2`

`B^2-48B+576=0`

`B^2-24B-24B+576=0`

`(B-24)(B-24)=0`

`B=24`

Therefore, 2nd worker will take 24 days to complete the entire job.

`A=48-24=24`

Therefore, 1st worker will take 24 days to complete the entire job.