A can complete a work in 12 days, B in 15 days. When A and B worked alternatively, when started byOptions12 1/4days13 1/4days14 1/4days12 3/4days

The question seems to be asking how long it would take for A and B to complete a task if they worked on it alternately, starting with A. Here's how you can solve it:

Step 1: Determine how much of the work A and B can each do in a day. A can complete the work in 12 days, so A can do 1/12 of the work in a day. B can complete the work in 15 days, so B can do 1/15 of the work in a day.

Step 2: Determine how much work they can do together in two days (since they are working alternately). In two days, A and B can do (1/12 + 1/15) of the work. This simplifies to 9/60 + 4/60 = 13/60 of the work.

Step 3: Determine how many two-day periods it would take for them to complete the work. Since they can do 13/60 of the work in two days, it would take them (60/13) two-day periods to complete the work. This is approximately 4.62 two-day periods.

Step 4: Convert this to days. Since each two-day period is 2 days, it would take them 4.62 * 2 = 9.23 days to complete the work.

Step 5: Since they can't work a fraction of a day and A starts, we round up to the next whole day which is 10 days. But since B doesn't work a full day on the 10th day, we subtract the amount of work B would do in a day from the total work left after 9 days.

After 9 days, 9/60 of the work is left. B would do 4/60 of the work in a day, so after subtracting this, 5/60 of the work is left.

Step 6: Determine how long it would take A to do this remaining work. A can do 1/12 of the work in a day, so it would take A (5/60) / (1/12) = 1/4 of a day to do the remaining work.

So, the total time it would take for A and B to complete the work if they worked on it alternately, starting with A, is 9 days + 1/4 day = 9 1/4 days.

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