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A rate = B rate =   a

C rate = 12

1/12  + 1/a  + 1/a = 1/3     solve for a

2/a = 3/12

a/2 = 12/3

a = 24/3 = 8 hrs

so lets say the house is 36 and carol does 3 per hour then carol did 3*3=9 in the beginning so 27 is left and 25/2 =13.5 and 13.5 so 13.5/3 to get 4.5 and divide 4.5 by 36 to get \(\Huge{8}\) hours