Problem Solving

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

Is it (D)? 12/7

(1S + 1E)*2Hrs = Job Complete
(1S + 2F)*2Hrs = Job Complete

So 1 Elf does the Job of 2 fairies ( 1E = 2F)

(1E + 1F)*4 Hrs = Job Complete (Looking at this equation, it can be seen that in order for the job to be completed in 2 hours, you'll need twice as many elves and fairies

2(1E+1F)*2Hrs = Job Complete so,
(2E + 2F)*2Hrs = Job Complete (equating this equation with the 2nd equation, it can be seen that 1S = 2E. 1E = 2F so 1S = 4F

(1E+1S+1F)*X Hrs = Job complete
Equate this w/ 2nd equation:

(E+S+F)*X Hrs = (1S + 2F)*2Hrs

(2F+4F+F)*X Hrs = (4F + 2F)*2Hrs
7F*X Hrs = 12 F*Hrs

X = 12/7 Hrs (D)