Question 22738
Try this:

If Larry can destroy the room in 30 minutes, he can destroy 1/30 of the room in 1 minute.
If Moe can destroy the room in 40 minutes, he can destroy 1/40 of the room in 1 minute.
If Curly can destroy the room in 20 minutes, he can destroy 1/20 of the room in 1 minute.

So, together, they can destroy {{{1/30+1/40+1/20 = 13/120}}} of the room in 1 minute. 
Therefore, it will take them {{{120/13}}} minutes to destroy the room working together.

{{{120/13}}}minutes = 9 minutes and 13.8 seconds.