AMC8 2013

AMC8 2013 · Q7

AMC8 2013 · Q7. It mainly tests Ratios & proportions, Rates (speed).

Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?

Trey 和他妈妈在铁路道口停车让火车通过。当火车开始通过时，Trey 在前 10 秒内数到 6 节车厢。火车以恒定速度通过道口用了 2 分 45 秒。火车中最可能的车厢数是以下哪项？

(A) 60 60

(B) 80 80

(D) 120 120

(E) 140 140

Answer

Correct choice: (C)

正确答案：（C）

Solution

Clearly, for every $5$ seconds, $3$ cars pass. It's more convenient to have everything in seconds: $2$ minutes and $45$ seconds$=2\cdot60 + 45 = 165$ seconds. We then set up a ratio: \[\frac{3}{5}=\frac{x}{165}\] \[3(165)=5x\] \[x=3(33)=99\approx\boxed{\textbf{(C)}\ 100}.\]

显然，每 5 秒通过 3 节车厢。将时间统一为秒：$2$分钟$45$秒$=2\cdot60 + 45 = 165$秒。然后设比例： \[\frac{3}{5}=\frac{x}{165}\] \[3(165)=5x\] \[x=3(33)=99\approx\boxed{\textbf{(C)}\ 100}\]。

Topics