A alone can complete a work in 16 days and B alone can complete the work in 12 days. How many days will it take to complete the work if they work on alternate days starting from A.

Question

Mathematics

Mara Joseph

9 May, 01:11

A alone can complete a work in 16 days and B alone can complete the work in 12 days. How many days will it take to complete the work if they work on alternate days starting from A.

+1

Answers (1)

Know the Answer?

Warner · Answer 1

14 days

Step-by-step explanation:

1. Convert the amount of work person A and B can do respectively in one day into fractions.

A = 1/16 B = 1/12

2. Get both fractions to a common denominator using the least common multiple. This is 48.

1/16 * 3 = 3/48 1/12 * 4 = 4/48

3. Add both fractions to find out how much work will be done in two days. We are doing this because we are working in a pattern, and this will allow us to multiply, which is more time efficient than repeatedly adding 3 and then 4.

3/48 + 4/48 = 7/48

4. Figure out how many sets of two days work (7/48) will get them to 48/48 (100% done) or closest to it without being under. This would be 7 sets.

7/48 * 7 = 49/48

5. Multiply 7 by 2. We are doing this because we worked in sets of two days to account for A working and then B, since they are taking turns.

7 * 2 = 14

6. It will take them 14 days.