Question

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

Answer 1

Answer:

We get that the one fairie and the one elf and one  smurf  can build  a treehouse for 12/7 hours.

Step-by-step explanation:

From Exercise we have that  

- One smurf and one elf can build a treehouse together in two hours

- One smurf ane two fairies can build a treehouse together in two hours

- One elf and one fairie can build a treehouse together in four hours

We conclude that one  elf equal with two fairies.

We conclude three  fairies can build a treehouse together in four hours, therefore,  the one  fairie can build a treehouse  in 12 hours.

We conclude that 1.5 elf can build a treehouse in four hours, therefore the one elf can build a treehouse  in 6 hours .

We conclude that one smurf can build a treehouse in 3 hours.

The one  fairie  for 1h can build 1/12  a treehouse.

The one  elf   for 1h can build 1/6  a treehouse.

The one  smurf  for 1h can build 1/3  a treehouse.

Therefore, we get that the one fairie and the one elf and one  smurf  for 1h can build

1/12+1/6+1/3= 7/12 a treehouse.

Now we count for how many hours they can make the whole a treehouse. We have the following proportion:

7/12 : 1 = 1 : x

x · 7/12=1

x=12/7

We get that the one fairie and the one elf and one  smurf  can build  a treehouse for 12/7 hours.