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

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vsarun77

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23 Aug 2017, 10:45

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Somehow I found it very difficult to digest explanations above.

Let's put it in this way.
Take total work = 1.

1. one smurf and one elf.
time = 2 hrs, rate= (1/2) rate= work/time
2. one smurf and 2 fairies
time= 2 hrs, rate= (1/2)

This implies 1 elf= 2 fairy( from 1 and 2)

3. one elf and one fairy
time= 4 hrs, rate= (1/4)
Implies rate of 3 fairies= (1/4), from above.
ie; rate of 1 fairy= (1/4)/3= (1/12)

To get combined rate of 1 smurf, 1 elf and 1 fairy,
Add rate of 1 smurf & 1 elf from 1st point with rate of 1 fairy= (1/2)+(1/12)= (7/12)

Now Time= Work/Rate= 1/ (7/12)= 12/7...

audi006

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27 Sep 2018, 06:49

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srp

D
--

1 elf ~ 2 Fairys

elf completes job in x hrs
therefore (1 fairy and 1 elf) gives 1/2x + 1/x = 1/2, x = 6

time to complete job:
1 elf: 6 hrs
1 Fairy: 12 hrs
1 Smurf: 3 hrs (1/s + 1/6 = 1/2)

all 3 together (t hrs):
1/3 + 1/6 + 1/12 = 1/t
t = 12/7

since 1E = 2F, shoud'nt E=24 (because F=12)?

sharanjaymalkani

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21 Dec 2018, 15:03

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S+E = 1/2 and we know that E+F = 1/4 we also know that E= 2F
Now substitute value E into the equation E+F = 1/4
This makes it 2F+F= 1/4
F=1/12
therefore 1/12 + 1/2= 7/12
Reciprocate for total and the answer is 12/7
Answer: D

kt9696

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04 Jan 2020, 02:14

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JCLEONES

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

Let's say there are 8 units of work.

1S + 1E = 4 units/hour
1S +2F = 4 units/hour
1E + 1F = 2 units/hour

Substituting values of S, E and F, we get:

S= 8/3 units, E= 4/3 units, and F= 2/3 units

So, 1S + 1E + 1F = 8 units/ (8/3 + 4/3 + 2/3 units) = 12/7

Answer (D) 12/7 hours

GMATinsight

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16 Aug 2020, 23:22

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JCLEONES

Answer: Option D

Please check the video for the step-by-step solution.

GMATinsight's Solution

indbos

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14 Oct 2020, 03:25

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From (I) and (III), 1s = 1e + 2f = 4f

Please explain the above line...

Kinshook

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30 Dec 2022, 21:52

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Given: 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.

Asked: 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?

Let the number of days to complete the work by Smurf , elf and fairy be s, e & f respectively

1/s + 1/e = 1/2
1/s + 2/f = 1/2
1/e = 2/f: f= 2e
1/e + 1/f = 1/4
1/s + 2/e + 1/f = 1/s + 5/f = 1/2 + 1/4 = 3/4
3/f = 3/4 - 1/2 = 1/4: f=12: e=6
1/s = 1/2 - 1/6 = 2/6 = 1/3: s=3
1/s + 1/e + 1/f = 1/3 + 1/6 + 1/12 = (4+2+1)/12 = 7/12

One smurf, one elf, and one fairy, working together, would take 12/7 hours to build the treehouse

IMO D

PalakFocus

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20 Apr 2025, 06:34

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What I ended up doing,

1S and 1E can anyway build it in 2 hours. F are the slowest, most of the work will be done by S & E. So the answer would be just under 2 hrs. From the question choices, A,B,E are instantly eliminated. Now its between C & D. 12/7 is closer to 2 than 10/7. Thus,D.

JCLEONES