Answer: 8 days.
Explanation:
Given that Anna can do a job in 4 days. After she has worked for 1 day, she is joined by Sylvia, and it takes them 2 days working together to finish the job.
Since Anna has already worked for 1 day, she would have worked the remaining days for 3 days. But she is joined by Sylvia, and it takes them 2 days working together to finish the job.
That is,
1/3 + 1/S = 1/2
Where S is the number of days Sylvia to do the job being completed in 2 days.
1/S = 1/2 - 1/3
1/S = (3 - 2)/6
1/S = 1/6
S = 6
The job Anna would have done for 3 days, will take 6 days for Sylvia.
The 1 days used by Anna will be 2 days for Sylvia.
Therefore, the total days that will take Sylvia to do the whole job by herself will be 2 + 6 = 8 days