Timothy and two friends are digging identical holes in a field. 
When Timothy works with Urban, they dig 1 hole in 4 days.  When 
Timothy works with Vincent, they dig 1 hole in 3 days.  When 
Urban works with Vincent, they dig 1 hole in 2 days.  When 
Timothy works alone, how long does it take him to dig 1 hole? 

.
.

Finger pointing down from darrell94590 on 1/2/2006

.
 
 
 

Drawing from Ripleys-Believe It Or Not

..

              THE SOLUTION
 

In 1 day; Timothy and Urban dig 1/4 a hole;
          Timothy and Vincent dig 1/3 a hole; 
          Urban and Vincent dig 1/2 a hole. 

Let us use Timothys twin brother who would do the same amount of
work if he were here.  If Timothy, his brother, Urban, and Vincent
work together for one day, they dig; 1/4 + 1/3 = 7/12 of a hole.
Since Urban and Vincent dig 6/12 of a hole per day, Timothy and
his brother dig 1/12 of a hole per day.  Then Timothy alone digs
1/24 of a hole per day.  Thus, Timothy can dig a hole in 24 days.