AMC 8 2018 Problem 12
AMC8 2018 年第 12 题
比与比例★★★☆☆
The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?
的汽车上的钟表是不准确的，以一个恒定的速度增加时间。一天当他开始购物时，他发现他汽车上的钟表和他的手表(手表是准确的)的读数都是中午 12：00．当他结束购物后，他的手表读数是 12：30，而他的汽车钟表显示 12：35．那一天晚些时候，Sri 丢了手表，他看了看汽车钟表，读数为晚上 7：00，则实际时间是晚上几点？
- A.5:50
- B.6:00
- C.6:30
- D.6:55
- E.8:10
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
We see that every 35 minutes the clock passes, the watch passes 30 minutes. That means that the clock is as fast the watch, so we can set up proportions. . Cross-multiplying we get x=6. Now, this is obviously redundant, because we could just eyeball it to see that the watch would have passed 6 hours. But this method is better when the numbers are a bit more complex, which makes it both easier and reliable. Either way, our answer is . --BakedPotato66
The ratio of the car clock to the watch clock is a ratio of 35:30 or 7:6 due to the clock being ahead by 5 minutes after 30 minutes has passed. This means that when the car clock passes 7 hours, the watch has passed 6 hours, meaning that the time would be . by SHREYU.MEDATATI
From 12:00 pm (noon) to 7:00 pm, the car clock has passed 12 35-minute cycles (12 X 35 = 420) because 7 hours = 420 minutes. So, 12 30-minute cycles (12 X 30 = 360) for the watch time are 360 minutes, which is 6 hours. Therefore, 6 hours added to 12:00 pm (noon) makes the answer . 7 hours have passed since 12:00 pm and 7 hours = 420 minutes because there are 60 minutes in an hour. Because every 35 minutes, the clock is ahead by 5 minutes, you need to divide 420 by 35 to find out how many times it happens. 420 divided by 35 is 12. Then you would multiply 12 by 5 because the clock is ahead by 5 minutes. 12 times 5 is 60, so that means that the clock is ahead by 60 minutes. In order to find the watch's time, you must find what was 60 minutes earlier than 7:00 which is .
If his car clock says it's 12:35 when it's actually 12:30, then that means that the car clock gains 10 minutes for every actual hour that has passed. Then, with this knowledge, you can make a chart: Actual Time | Car Clock 12:00 | 12:00 1:00 | 1:10 2:00 | 2:20 3:00 | 3:30 2:00 | 2:20 3:00 | 3:30 4:00 | 4:40 5:00 | 5:50 6:00 | 7:00 As you can see, the answer is .žen D.
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