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 $=\frac{1}{8}$
(B+C)'s 1 day work $=\frac{1}{12}$
(A+C)'s 1 day work $=\frac{1}{16}$
$\therefore$ [(A+B)+(B+C)+(A+C)]'s 1 day work
$=\frac{1}{8}+\frac{1}{12}+\frac{1}{16}$
i.e. [A+B+B+C+A+C]'s 1 day work
$=\frac{1}{8}+\frac{1}{12}+\frac{1}{16}$
$=\frac{6+4+3}{48}=\frac{13}{48}$
i.e. 2(A+B+C)'s 1 day work $=\frac{13}{48}$
i.e. (A + B + C)'s 1 day work $=\frac{13}{48}\times \frac{1}{2}=\frac{13}{96}$
$\therefore$ (A + B + C) can do the work in $=\frac{96}{13}$ days
$=7\frac{5}{13}$ days.