Question

Question:
A&B can do a job in 12 days, B & C in 15 days and C&A in 20 days. How long would A take to do that work?
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Answer 1

Answer:

$(a + b) \: 1 \: day \: work \: = \frac{1}{12} \\ \\ (b + c) \: 1 \: day \: work = \frac{1}{15} \\ \\ (c + a) \: 1 \: day \: work = \frac{1}{20} \\ \\ 2(a + b + c) \: 1 \: day \: work = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5 + 4 + 3}{60} = \frac{12}{60} = \frac{1}{5} \\ \\ a \: 1 \: day \: work \: = \frac{1}{5} - \frac{1}{15} = \frac{3 - 1}{15} = \frac{2}{15} \\ \\ answer = \frac{15}{2} = 7 \frac{1}{2} days$

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