题目

There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?


选项

A.

10min

B.

12min

C.

15min

D.

18min

E.

20min

解析

“a”单独完成这项工作需要90分钟。 “a”的工作效率 = \( \frac{1}{90} \) “b”单独完成这项工作需要45分钟。 “b”的工作效率 = \( \frac{1}{45} \) “c”单独完成这项工作需要30分钟。 “c”的工作效率 = \( \frac{1}{30} \) “a、b、c”三人合作的工作效率为: \[ \frac{1}{90} + \frac{1}{45} + \frac{1}{30} = \frac{1+2+3}{90} = \frac{6}{90} = \frac{1}{15} \] 因此,三人合作完成这项工作所需的时间为: \[ \frac{1}{(1/15)} = 15 \text{分钟} \] 答案:C
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