If 6 cats can kill 6 rats in 6 minutes, how many cats will be needed to kill 100 rats in 50 minutes?

 Start with 6 cats kill 6 rats in 6 minutes, so it takes 6 minutes for 1 cat to kill 1 rat 
1 cat kills 1 rat in 6 minutes 
now extend this rate to 50 minutes (* 8 1/3) 
1 cat kills 8 1/3 rats in 50 minutes and finally multiply by 12 to get the number of cats necessary to kill 100 rats in 50 minutes 
12 cats kill 100 in 50 minutes 
if 6 cats kill 6 rats in 6 minutes, then 
12 cats kill 12 rats in 6 minutes << double the number of cats>> 
now multiply time by 8 1/3 to get to 50 minutes, and therefore the number of rats killed multiplied by 8 1/3 
yep, these 12 cats will kill 100 rats in 50 minutes

It will take 12 rats to kill 100 rats in 50 minutes