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# Working together at their respective rates, machine A, B,

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Current Student
Joined: 11 May 2008
Posts: 544
Working together at their respective rates, machine A, B,  [#permalink]

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22 Jul 2008, 10:46
1
Working together at their respective rates, machine A, B, and C can finish a certain work in 8/3 hours. How many hours will it take A to finish the work independently?
(1) Working together, A and B can finish the work in 4 hours.
(2) Working together, B and C can finish the work in 48/7 hours.

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Intern
Joined: 08 Jul 2008
Posts: 14

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22 Jul 2008, 11:00
given 1/A + 1/B+1/C = 3/8 [1]
find A:

1st statement is not sufficient as we ve 1/A + 1/B = 1/4 , we don't ve the value of 1/C so that we can substitute in in [1]

2nd statement is sufficient as we have 1/B + 1/C = 7/48, We can subsitute this in equation [1] and find the value of a:
1/A + 7/48 = 3/8
=> 1/A = 11/48
=> A = 48/11
VP
Joined: 28 Dec 2005
Posts: 1439

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22 Jul 2008, 14:27
B for me as well, same reasoning as above
Director
Joined: 12 Jul 2008
Posts: 501
Schools: Wharton

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22 Jul 2008, 14:39
RayOfLight wrote:
given 1/A + 1/B+1/C = 3/8 [1]
find A:

1st statement is not sufficient as we ve 1/A + 1/B = 1/4 , we don't ve the value of 1/C so that we can substitute in in [1]

2nd statement is sufficient as we have 1/B + 1/C = 7/48, We can subsitute this in equation [1] and find the value of a:
1/A + 7/48 = 3/8
=> 1/A = 11/48
=> A = 48/11

I get B, but with a different reasoning:

1:
1/A + 1/B = 1/4
1/A + 1/B + 1/C = 3/8
1/4 + 1/C = 3/8
1/C = 1/8

1/A + 1/B + 1/8 = 3/8 -- now you're stuck because you don't know the ratio of A:B or the value of B.

2:
1/A + 1/B + 1/C = 3/8
1/A + 7/48 = 3/8
1/A = 11/48
A = 48/11

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This discussion does not meet community quality standards. It has been retired.

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Non-Human User
Joined: 09 Sep 2013
Posts: 9835
Re: Working together at their respective rates, machine A, B,  [#permalink]

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03 Feb 2019, 11:21
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Re: Working together at their respective rates, machine A, B,   [#permalink] 03 Feb 2019, 11:21
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