A, B and C can do a piece of work in 6 days, 12 days and 24 days respectively. In what time will they all together do it?

A can do a piece of work in = 6 days
B can do a piece of work in = 12 days
C can do a piece of work in = 24 days
$\therefore$ A's 1 day work $=\frac{1}{6}$
$\therefore$ B's 1 day work $=\frac{1}{12}$
$\therefore$ C's 1 day work $=\frac{1}{24}$
(A+B+C)'s 1 day work $=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}$
$=\frac{4+2+1}{24}=\frac{7}{24}$
$\therefore$ (A + B + C) can do the work in $=\frac{24}{7}$ days
$=3\frac{3}{7}$ days