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

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Intern
Joined: 25 Jan 2016
Posts: 1
Re: One smurf and one elf can build a treehouse together in two  [#permalink]

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23 Aug 2017, 10:45
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...
Intern
Joined: 05 May 2017
Posts: 5
Re: One smurf and one elf can build a treehouse together in two  [#permalink]

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27 Sep 2018, 06:49
srp wrote:
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)?
Intern
Joined: 19 Dec 2018
Posts: 1
Re: One smurf and one elf can build a treehouse together in two  [#permalink]

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21 Dec 2018, 15:03
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
Re: One smurf and one elf can build a treehouse together in two   [#permalink] 21 Dec 2018, 15:03

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