题目

Working alone, it takes Randy 11 hours to inventory the instrument shop. Liz can complete the same inventory in 10 hours. If they worked together, how long would it take them to complete the inventory of the instrument shop?


选项

A.

5.24 hours

B.

5.59 hours

C.

5.77 hours

D.

5.6 hours

E.

5 hours

解析

效率 × 时间 = 工作量 兰迪的效率为\(\frac{1}{11}\)台乐器/小时,莉兹的效率为\(\frac{1}{10}\)台乐器/小时。 如果两人一起工作,总效率为\(\left(\frac{1}{11} + \frac{1}{10}\right)\)台乐器/小时。 时间 = 工作量 ÷ 效率 \[ \begin{align*} &= 1 \div \left(\frac{1}{11} + \frac{1}{10}\right) \\ &= 1 \div \frac{21}{110} \\ &= \frac{110}{21} \\ &= 5.24 \text{ 小时} \end{align*} \]
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