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Mathematics

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 can they do it, all working together?

Direct & Inverse Variations

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Answer

(A + B)'s 1 day work = 18\dfrac{1}{8}

(B + C)'s 1 day work = 112\dfrac{1}{12}

(C + A)'s 1 day work = 116\dfrac{1}{16}

2(A + B + C)'s 1 day work = 18+112+116\dfrac{1}{8} + \dfrac{1}{12} + \dfrac{1}{16}

= 6+4+348\dfrac{6 + 4 + 3}{48}

= 1348\dfrac{13}{48}

(A + B + C)'s 1 day work = 1348×2\dfrac{13}{48 \times 2}

= 1396\dfrac{13}{96}

No. of days to complete the work when A, B and C are working together = 9613=7513\dfrac{96}{13} = 7\dfrac{5}{13}

Hence, A, B and C working together can complete the work in 75137\dfrac{5}{13} days.

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