GMAT
题目
Two pools in the shape of rectangular prisms are being filled with water by pumps. The first pump fills its pool completely in one hour. The second pumps water twice as fast as the first pump, and fills a pool that is twice the width, twice the length, and the same depth of the first pool. How many hours does it take the second pump to fill its pool?
解析
对于水泵1：
\(W_1 =\) 泳池的容积
\(T_1 = 1\) 小时
\(R_1 =\) 泳池的注水速度
因此，\(T_1 = \frac{W_1}{R_1}\)
对于水泵2：
\(W_2 = 4W_1\)（泳池的宽和长均变为原来的2倍，容积变为原来的4倍）
\(R_2 = 2R_1\)（注水速度变为原来的2倍）
因此，\(T_2 = \frac{W_2}{R_2}\)
\[
T_2 = \frac{4W_1}{2R_1} = 2 \cdot \frac{W_1}{R_1} = 2T_1 \quad (\text{由上述水泵1的公式推导})
\]
因此，如果水泵1需要1小时注满，那么水泵2需要2小时。
答案为选项B。
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