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Question
A and B can do a work in 8 days; B and C in 12 days, and A and C in 16 days. In what time could they do it, all working together?
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Solution
A and B can do a work in = 8 days
B and C can do a work in = 12 days
A and C can do a work in = 16 days
(A+B)’s 1-day work =`1/8`
(B+C)’s 1-day work =`1/12`
(A+C)'s 1-day work =`1/16`
∴ [(A+B)+(B+C)+(A+C)]'s 1 day work
`=1/8+1/12+1/16`
i.e. [A+B+B+C+A+C]'s 1 day work
`=1/8+1/12+1/16`
`=(6+4+3)/48=13/48`
i.e. 2(A+B+C)'s 1-day work =`13/48`
i.e. (A+B+C)'s 1-day work =`13/48xx1/2=13/96`
∴ (A+B+C) can do the work in =`96/13`days
`=7 5/13` days
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