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. How long would it have taken Sylvia to do the whole job by herself?

8 days.

Step-by-step 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