SOLUTION: If 3 people can paint 2 rooms in 4 days, how many people are needed to paint 12 rooms in 6 days?

3 people can paint 2 rooms in 4 days, so 
3 people can paint 6 rooms in 12 days. Therefore,
6 people can paint 12 rooms in 12 days, so
12 people can paint 12 rooms in 6 days.

ANSWER: 12 people

You can also use the worker-time-job formula, which is:



where

W1 = the number of workers in the first situation.
T1 = the number of time units (days in this case) in the first situation.
J1 = the number of jobs in the first situation.

W2 = the number of workers in the second situation.
T2 = the number of time units (days in this case) in the second situation.
J2 = the number of jobs in the second situation.

W1 =  3             W2 = the unknown quantity     
T1 =  4             T2 = 6 
J1 =  2             J2 = 12







 reduces to  and  reduces to 



Multiply both sides by 2:

Answer = W2 = 12 workers.  (or 'people').

Edwin

I think the easiest way is to use the fact that 

 is always a constant.   

, so 6 is the constant.

So put x for the unknown, in this case the number of workers, 
and set it equal to the constant 6







Edwin
   

We want to solve the problem by writing a proportion.



    What quantity is the same to equate two sides of proportion ?

        - The rate of work is the same per day and per worker.



When 3 workers paint 2 rooms in 4 days, the rate of work is   =  = .


When x workers paint 12 rooms in 6 days, the rate of work is   = .


These two rates of work we want to equate (since they are equal)

     = .


From this proportion,  x = 2*6 = 12 workers.


ANSWER.  12 workers are needed.