Since 6 men can dig a trench in 3 days, 3 times as many men, or 18 men,
can do it in 1/3 the time or just 1 day.

So half of 18 men, or 9 men, will take twice as long as 18 men, or 2 days.

--------------------------------------------------------

Another way to do it is that this fraction must stay constant:

WORKERS × TIME     WORKERS × TIME
——————————————  = ——————————————    
     JOBS               JOBS


     6 × 3            9 × T 
     —————     =     ————————
       1                1

       18            9T 
      ———     =     —————
       1             1
 
       18    =     9T

        2    =     T

   
2 days.

Edwin