AMC8 2022

AMC8 2022 · Q7

AMC8 2022 · Q7. It mainly tests Decimals, Rates (speed).

When the World Wide Web first became popular in the $1990$s, download speeds reached a maximum of about $56$ kilobits per second. Approximately how many minutes would the download of a $4.2$-megabyte song have taken at that speed? (Note that there are $8000$ kilobits in a megabyte.)

当万维网在$1990$年代首次流行时，下载速度最高约为每秒$56$千比特。一个$4.2$兆字节的歌曲在这个速度下大约需要下载多少分钟？（注意1兆字节有$8000$千比特。）

(A) 0.6 0.6

(B) 10 10

(D) 7200 7200

(E) 36000 36000

Answer

Correct choice: (B)

正确答案：（B）

Solution

Notice that the number of kilobits in this song is $4.2 \cdot 8000 = 8 \cdot 7 \cdot 6 \cdot 100.$ We must divide this by $56$ in order to find out how many seconds this song would take to download: $\frac{\cancel{8}\cdot\cancel{7}\cdot6\cdot100}{\cancel{56}} = 600.$ Finally, we divide this number by $60$ because this is the number of seconds to get the answer $\frac{600}{60}=\boxed{\textbf{(B) } 10}.$

注意这首歌的千比特数是$4.2 \cdot 8000 = 8 \cdot 7 \cdot 6 \cdot 100$。我们必须除以$56$来计算下载这首歌需要多少秒：$\frac{\cancel{8}\cdot\cancel{7}\cdot6\cdot100}{\cancel{56}} = 600$。最后，除以$60$得到分钟数：$\frac{600}{60}=\boxed{\textbf{(B) } 10}$。

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