Answer:
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.
