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# Three machines, K, M, and P, working simultaneously and

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Three machines, K, M, and P, working simultaneously and [#permalink]  03 Dec 2012, 02:40
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Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes.
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.
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Re: Three machines, K, M, and P, working simultaneously and [#permalink]  03 Dec 2012, 02:42
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Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> \frac{1}{m}+\frac{1}{p}=\frac{1}{36}, thus \frac{1}{k}+\frac{1}{36}=\frac{1}{24} --> we can find the value of k. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> \frac{1}{k}+\frac{1}{p}=\frac{1}{48}. The value of k cannot be determined from the data we have. Not sufficient.

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Re: Three machines, K, M, and P, working simultaneously and [#permalink]  04 Mar 2013, 01:57
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes.
RATE K + M + P) - RATE : (M+P) = RATE : K. SUFFICIENT
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.
RATE K + M + P) - RATE : (K+P) = RATE : M. NOT SUFFICIENT
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Re: Three machines, K, M, and P, working simultaneously and [#permalink]  28 Nov 2013, 05:29
Bunuel wrote:
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> \frac{1}{m}+\frac{1}{p}=\frac{1}{36}, thus \frac{1}{k}+\frac{1}{36}=\frac{1}{24} --> we can find the value of k. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> \frac{1}{k}+\frac{1}{p}=\frac{1}{48}. The value of k cannot be determined from the data we have. Not sufficient.

I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way?

Let Rk, Rm and Rp be the rates for the machines K,M and P respectively.
Then 1/Rk +1/Rm+1/Rp = 24

St 1 gives ---> 1/Rm + 1/Rp = 36

So, we get 1/Rk + 36 = 24.

Solving, 1/Rk = 24-36=-12

Why am I getting a negative value?
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Re: Three machines, K, M, and P, working simultaneously and [#permalink]  29 Nov 2013, 09:12
Expert's post
audiogal101 wrote:
Bunuel wrote:
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> \frac{1}{m}+\frac{1}{p}=\frac{1}{36}, thus \frac{1}{k}+\frac{1}{36}=\frac{1}{24} --> we can find the value of k. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> \frac{1}{k}+\frac{1}{p}=\frac{1}{48}. The value of k cannot be determined from the data we have. Not sufficient.

I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way?

Let Rk, Rm and Rp be the rates for the machines K,M and P respectively.
Then 1/Rk +1/Rm+1/Rp = 24

St 1 gives ---> 1/Rm + 1/Rp = 36

So, we get 1/Rk + 36 = 24.

Solving, 1/Rk = 24-36=-12

Why am I getting a negative value?

1/Rk, 1/Rm, and 1/Rp are the numbers of minutes machines K, M, and P take to complete the task alone. Each must be greater than the time needed for three machines to complete a certain task together (24 minutes), thus 1/Rk +1/Rm+1/Rp = 24 is not right. The same for 1/Rm + 1/Rp = 36.

Hope it's clear.
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Re: Three machines, K, M, and P, working simultaneously and [#permalink]  29 Nov 2013, 21:35
Bunuel wrote:
audiogal101 wrote:
Bunuel wrote:
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> \frac{1}{m}+\frac{1}{p}=\frac{1}{36}, thus \frac{1}{k}+\frac{1}{36}=\frac{1}{24} --> we can find the value of k. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> \frac{1}{k}+\frac{1}{p}=\frac{1}{48}. The value of k cannot be determined from the data we have. Not sufficient.

I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way?

Let Rk, Rm and Rp be the rates for the machines K,M and P respectively.
Then 1/Rk +1/Rm+1/Rp = 24

St 1 gives ---> 1/Rm + 1/Rp = 36

So, we get 1/Rk + 36 = 24.

Solving, 1/Rk = 24-36=-12

Why am I getting a negative value?

1/Rk, 1/Rm, and 1/Rp are the numbers of minutes machines K, M, and P take to complete the task alone. Each must be greater than the time needed for three machines to complete a certain task together (24 minutes), thus 1/Rk +1/Rm+1/Rp = 24 is not right. The same for 1/Rm + 1/Rp = 36.

Hope it's clear.

Got it. So would it be correct to say that 1/ (Rk+Rm+Rp) = 24? (since the denominator has combined rate now)?
Re: Three machines, K, M, and P, working simultaneously and   [#permalink] 29 Nov 2013, 21:35
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