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MrMuchimi
2 years ago
12

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.
Mathematics
1 answer:
Agata [3.3K]2 years ago
8 0

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.

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