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  3. Working alone at its constant rate, machine A takes 3 hours to produce a batch o

Working alone at its constant rate, machine A takes 3 hours to produce a batch o

游客2025-02-23  19
问题 Working alone at its constant rate, machine A takes 3 hours to produce a batch of identical computer parts. Working alone at its constant rate, machine B takes 2 hours to produce an identical batch of parts. How long will it take the two machines, working simultaneously at their respective constant rates, to produce an identical batch of parts?
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答案 6/5 hours, or 1 hour 12 minutes
解析 Since machine A takes 3 hours to produce a batch, machine A can produce 1/3 of the batch in 1 hour. Similarly, machine B can produce - of the batch in 1 hour. If we let x represent the number of hours it takes both machines, working simultaneously, to produce the batch, then the two machines will produce - of the job in 1 hour. When the two machines work together, adding their individual production rates, 1/3 and 1/2, gives their combined production rate 1/x. Therefore,

Thus, working together, the machines will take 6/5 hours, or 1 hour 12 minutes, to produce a batch of parts.
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