A and B can do a piece of work in 24 days, B and C in 30 days, and C and A in 40 days. How long would all three together take to do the same work?

Let A, B, and C do $x$, $y$, and $z$ work per day. Then $x+y=1/24$, $y+z=1/30$, and $x+z=1/40$. Adding gives $2(x+y+z)=1/24+1/30+1/40=1/10$. So $x+y+z=1/20$. Therefore all three together take 20 days.