Machine A can produce of a ton of paintbrushes in one hour

题目

Machine A can produce of a ton of paintbrushes in one hour. Machine B can produce of a ton of paintbrushes in one hour. Working together at their individual rates, how long would it take the two machines to produce 2 tons of paintbrushes?

选项

8 hours

8 hours 24 minutes

9 hours

9 hours 46 minutes

12 hours

解析

两人的总效率 = \(\frac{1}{6} + \frac{1}{14} = \frac{7}{42} + \frac{3}{42} = \frac{10}{42} = \frac{5}{21}\) 吨/小时我们需要生产2吨时间 = 产量 ÷ 效率 \[ \begin{align*} &= 2 \div \frac{5}{21} \\ &= 2 \times \frac{21}{5} \\ &= \frac{42}{5} \\ &= 8\frac{2}{5} \text{ 小时} \\ &= 8 \text{ 小时 } 24 \text{ 分钟} \end{align*} \] 答案：B

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