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

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Re: Three machines, K, M, and P, working simultaneously and [#permalink]
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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.