A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in ______.

Sure, let's solve this step by step.

Step 1: First, we need to find out how much work A and B can do in a day.

A can complete the work in 16 days, so A's work rate is 1/16 of the work per day. B can complete the work in 12 days, so B's work rate is 1/12 of the work per day.

Step 2: Now, let's find out how much work they can do together in two days (since they are working on alternate days).

In two days, A and B together can do (1/16 + 1/12) = 7/96 of the work.

Step 3: Now, we need to find out how many such two-day pairs it will take to complete the work.

To find this, we divide 1 (the total work) by the work done in two days. So, 1/(7/96) = 96/7 ≈ 13.71.

Since they can't work for a fraction of a day, we round this up to the nearest whole number, which is 14.

Step 4: However, this is the number of two-day pairs, so the total number of days it will take to complete the work is 14 * 2 = 28 days.

So, starting with A, they will complete the work in 28 days.

Sure, let's solve this step by step.

Step 1: First, we need to find out how much work A and B can do in a day.

A can complete the work in 16 days, so A's one day work is 1/16. B can complete the work in 12 days, so B's one day work is 1/12.

Step 2: Now, let's find out how much work they can do together in two days (since they are working on alternate days).

In two days, A and B can do (1/16 + 1/12) work. To add these two fractions, we need to find a common denominator. The least common multiple of 16 and 12 is 48. So, the work they can do in two days is (3/48 + 4/48) = 7/48.

Step 3: Now, we need to find out how many such two-day pairs it will take to complete the work.

Since they can do 7/48 of the work in two days, the number of two-day pairs it will take to complete the work is 1 / (7/48) = 48/7 = 6.857 pairs.

Step 4: But we can't have a fraction of a two-day pair. So, we need to round up to the nearest whole number, which is 7 pairs. This means it will take 14 days for them to complete the work together.

Step 5: But remember, we rounded up. This means that after 14 days, they have done a little more than the work required. So, on the 14th day, A starts working and completes the work before the day is over.

So, the total work will be completed in less than 14 days.

To solve this problem, we first need to find out how much work A and B can do in one day.

1. A's one day work = 1/16
2. B's one day work = 1/12

Next, we find out how much work they can do together in two days (since they are working on alternate days).

3. A and B's two day work = A's one day work + B's one day work = 1/16 + 1/12 = 7/96

Now, we need to find out how many such two-day pairs it will take to complete the work.

4. Number of two-day pairs = 1 / (A and B's two day work) = 1 / (7/96) = 96/7 = 13.71

Since we can't have a fraction of a day, we round this up to 14 two-day pairs.

But remember, this is the number of two-day pairs, so the total number of days is 2 * 14 = 28 days.

So, starting with A, they will complete the work in 28 days.