SOLUTION: When Raul and Rudy work together, they can point a car in 8 days. Also, they could point this car if Raul worked 12 days and Rudy worked 6 days. How long would it take each of them

Let "x" be the Raul's rate of work and "y" be Rudy's rate of work
( measured in the unit "car-per-day,  ).

Then from the condition you have this system of two linear equations

x + y = ,      (1)    ( "When Raul and Rudy work together, they can point a car in 8 days." )
12x + 6y = 1.     (2)    ( "they could point this car if Raul worked 12 days 
and Rudy worked 6 days." )

To solve it, express x =  from (1) and substitute it into (2). You will get

 + 6y = 1,  or

3 - 24y + 12y = 2,  or

3 - 12y = 2,  or  3 - 2 = 12y,  or  y = .

Thus you found that the Rudy's rate is .  Hence, he need 12 days to complete the job working alone.

Next, from (1) x =  =  = .

It means that Raul's rate is , and Raul needs 24 days to complete the job working alone.

Answer.  Raul needs 24 days to complete the job working alone.
         Rudy needs 12 days to complete the job working alone.