GMAT
题目
The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 15 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
解析
### 第一种方法：
设三个小时的流量速率分别为\( a \)、\( b \)、\( c \)。
- 第二个小时的流量速率\( b = 15 \)加仑/小时。
- 第二个小时的流量速率比第一个小时快50%，即\( b = \frac{3}{2}a \)。
代入\( b = 15 \)，得：\( 15 = \frac{3}{2}×a \)，解得\( a = 10 \)加仑/小时。
- 第三个小时的流量比第二个小时多25%，即\( c = \frac{5}{4}×15 = \frac{75}{4} = 18.75 \)加仑/小时。
总流量速率 = \( a + b + c = 10 + 15 + 18.75 = 43.75 \)
选项：C
### 第二种方法：
可用比例求解。
- \( a:b = 2:3 \)
- \( b:c = 4:5 \)
统一比例得：\( a:b:c = 8:12:15 = 8x:12x:15x \)，总比例为\( 35x \)。
已知\( 12x = 15 \)，解得\( x = \frac{5}{4} = 1.25 \)。
总流量速率 = \( 35x = 35×1.25 = 43.75 \)
选项：C
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