SOLUTION: A and b can paint a wall in 2 hours A and C can paint the wall in 3 hours B and C can paint the wall in 4 hours How long will it take to paint the wall if all 3 work together

Let a be the A's rate of work (the part of the job per hour).

Let b ve the B's rate of work;

and let c be the C's rate of work.


We have from the condition

    a + b =     (1)

    a + c =     (2)

    b + c =     (3)


Add equations (1), (2) and (3) (both sides). You will fet

    2a + 2b + 2c =  =  = ;

hence

    a + b + c = .    (4)


From equation (4), subtract equation (4).  You will get

    c =  =  = ;  hence c = .


From equation (4), subtract equation (2).  You will get

    b =  =  = ;  hence b = .


From equation (4), subtract equation (3).  You will get

    a =  =  = ;  hence a = .


ANSWER.  It will take   hours for A to complete the job working alone;

         It will take   hours for B to complete the job working alone;

         It will take   hours for C to complete the job working alone.