题目

Ed's own pump, operating alone at its constant rate, can empty his swimming pool in 15 hours. The pump Ed rented, operating alone at its constant rate, can empty his swimming pool in 5 hours. How many hours will it take the two pumps, operating simultaneously and independently at their respective constant rates, to empty Ed's pool?


选项

A.

3

B.

C.

D.

E.

4

解析

假设埃德自己的水泵效率是\( x \)泳池/小时,租赁水泵的效率是\( y \)泳池/小时,那么: \[ x = \frac{1}{15} \] \[ y = \frac{1}{5} \] 将两者效率相加,得到两台水泵的合效率: \[ x + y = \frac{1}{15} + \frac{1}{5} = \frac{4}{15} \] 因为效率是时间的倒数,所以两台水泵排空泳池所需的时间为\( \frac{15}{4} = 3\frac{3}{4} \)小时。 答案:D 另一种思路:租赁水泵的速度是埃德水泵的3倍,相当于3台埃德水泵的效率。因此,两台水泵一起工作时,相当于\( 1 + 3 = 4 \)台埃德水泵同时工作。4台埃德水泵排空泳池的时间为\( \frac{15}{4} = 3\frac{3}{4} \)小时。 答案:D
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