One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two

One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two fairies in order to complete the same job in the same amount of time. If one elf and one fairy worked together, it would take them four hours to build the treehouse. Assuming that work rates for smurfs, elves, and fairies remain constant, how many hours would it take one smurf, one elf, and one fairy, working together, to build the treehouse?

(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7

One Elf's rate + One Smurf's rate = 2 Fairies' rate + One Smurf's rate

One Elf's rate , E = 2 Fairies' rate, F

E = 2F

(E+F)*4 = T (T= work required to finish tree house) ------- (1)
(E+S)*2 = T --------- (2)
(2F+S)*2 = T ------ (3)


Solving we get E=T/6, S=T/3 and F =T/12 now we have to find T/(E+S+F) = T/T (1/(1/3+1/6+1/12) = 1/(7/12) = 12/7