If both valves are open simultaneously, they can fill an empty pool in 48 minutes

题目

If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?

选项

9,000 cubic meters

10,500 cubic meters

11,750 cubic meters

12,000 cubic meters

12,500 cubic meters

解析

设第一个阀门的注水速率为\( x \)立方米/分钟，则第二个阀门的注水速率为\( x + 50 \)立方米/分钟。已知两个阀门一起注满泳池需要48分钟，因此泳池的容量可表示为： \( C = 时间 × 合速率 = 48 × (x + x + 50) = 48(2x + 50) \) 由于第一个阀门单独注满泳池需要2小时（即120分钟），泳池容量也可表示为： \( C = 时间 × 速率 = 120x \) 将两个表示\( C \)的式子联立，得： \( 120x = 48(2x + 50) \) 解得\( x = 100 \)，因此泳池容量\( C = 120x = 12000 \)立方米。答案：D

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