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04 Jan 2007, 13:47
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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
(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7
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04 Jan 2007, 14:11
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kidderek
it is 12/7
s + e take 2 hours
s + 2f take 2 hours
e + f take 4 hours
so, s + e + f take how many hours?
s + e = s + 2f
e = 2f
s + 2f = 2 (e + f)
s = 2e
now s = 2e = 4f, so (s + e + f) = 4f+2f+f = 7f
s + e = s + 2f = 4f+2f = 6f take 2 hours
7f take 2x6/7 hours = 12/7 hours
04 Jan 2007, 15:17
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We are given:
1/2 = 1/S + 1/E
1/2 = 1/S + 2/F
1/4 = 1/E + 1/F
We need to find:
1 / (1/S + 1/E + 1/F)
From the first 3 eqs:
1/S = 1/3; 1/E = 1/6; 1/F = 1/12. Replacing in the previous eq:
12/7.
D.
Note that you don´t need to find S, E or F. It´s enough to find the inverses (1/ ).
1/2 = 1/S + 1/E
1/2 = 1/S + 2/F
1/4 = 1/E + 1/F
We need to find:
1 / (1/S + 1/E + 1/F)
From the first 3 eqs:
1/S = 1/3; 1/E = 1/6; 1/F = 1/12. Replacing in the previous eq:
12/7.
D.
Note that you don´t need to find S, E or F. It´s enough to find the inverses (1/ ).
Archived Topic
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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