Machine K and Machine N, working simultaneously and independently at their respective constant rates, process of the shipment of a certain chemical product in 1

题目

Machine K and Machine N, working simultaneously and independently at their respective constant rates, process of the shipment of a certain chemical product in 1.6 hours. Then machine K stopped working, and Machine N, working alone at it's constant rate, processed the rest of the shipment in 2 hours. How many hours would it have taken Machine K, working alone at its constant rate, to process the entire shipment?

选项

3.8

4.0

4.8

5.4

6.0

解析

机器N单独工作2小时，处理了这批货物的\( 1 - \frac{2}{3} = \frac{1}{3} \)。因此，在1.6小时内，它处理的货物量为：\( 时间 × 速率 = 1.6 × \frac{\frac{1}{3}}{2} = \frac{4}{5} × \frac{1}{6} = \frac{4}{15} \)。所以，在1.6小时内，剩余\( \frac{2}{3} - \frac{4}{15} = \frac{2}{5} \)的货物是由机器K处理的。因此，机器K单独处理整批货物所需的时间为：\( \frac{1}{\frac{2}{5}} × 1.6 = \frac{5}{2} × \frac{8}{5} = 4 \)小时。答案：B

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