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?

Answer 1

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 =${\displaystyle \frac{1}{8}}$

(B+C)’s 1-day work =${\displaystyle \frac{1}{12}}$

(A+C)'s 1-day work =${\displaystyle \frac{1}{16}}$

∴ [(A+B)+(B+C)+(A+C)]'s 1 day work

${\displaystyle =\frac{1}{8}+\frac{1}{12}+\frac{1}{16}}$

i.e. [A+B+B+C+A+C]'s 1 day work

${\displaystyle =\frac{1}{8}+\frac{1}{12}+\frac{1}{16}}$

${\displaystyle =\frac{6+4+3}{48}=\frac{13}{48}}$

i.e. 2(A+B+C)'s 1-day work =${\displaystyle \frac{13}{48}}$

i.e. (A+B+C)'s 1-day work =${\displaystyle \frac{13}{48}\times \frac{1}{2}=\frac{13}{96}}$

∴ (A+B+C) can do the work in =${\displaystyle \frac{96}{13}}$days

${\displaystyle =7\frac{5}{13}}$ days