GMAT
题目
There are two inlets and one outlet to a cistern. One of the inlets takes 3 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
解析
两个进水口的合计进水速率为\( \frac{1}{3} + \frac{1}{6} = \frac{1}{2} \)蓄水池/小时。
因此，一起工作时，注满蓄水池需要2小时（时间是速率的倒数）。
从上午9:00到10:30，共1.5（即\( \frac{3}{2} \)）小时，进水口可注入的水量为（时间×速率）= \( \frac{3}{2} × \frac{1}{2} = \frac{3}{4} \)蓄水池。
之后打开出水口，剩余\( \frac{1}{4} \)蓄水池的水用了1小时注满。
设出水口的排水速率为\( x \)，则有：\( \frac{1}{2} - x = \frac{1}{4} \)→解得\( x = \frac{1}{4} \)蓄水池/小时，这意味着出水口单独排空蓄水池需要4小时。
答案：E
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