it takes 4 hours for 9 cooks to prepare a school 
lunch. How long would it take 6 cooks to prepare the lunch?
it would take 6 cooks _____hours.
is it 2.66? 

Of course not!  Think about that answer, 2.66 hours! It takes 9 cooks 4
hours, so how could it take less time for 6 cooks than it took for 9 
cooks?

It would obviously take fewer cooks MORE time than 4 hours, not less time!
 
You should learn this rule:

The first check you should always make on your answer to any problem
is to determine whether the answer makes any sense! 2.66 does not.

Anyway, let x be the number of hours required.

>>...it takes 4 hours for 9 cooks to prepare a school lunch...<<

So, in one hour 9 cooks can prepare 1/4 of a school lunch

So, in one hour 1 cook can prepare 1/9th of 1/4, or 1/36th of a school 
lunch.

So, in x hours 1 cook can prepare x/36ths of a school lunch.

So, in x hours 6 cooks can prepare 6x/36ths of a school lunch.
That reduces to x/6ths of a school lunch

So, x/6's of a school lunch must total 1 school lunch.

Therefore   x/6 = 1 or x = 6 hours.

Edwin 
AnlytcPhil@aol.com