AMC 8 1986 Problem 1

AMC8 1986 年第 1 题

比与比例★☆☆☆☆

In July 1861, 366 inches of rain fell in Cherrapunji, India. What was the average rainfall in inches per hour during that month?

1861 年 7 月，印度 Cherrapunji 的降雨量为 366 英寸。该月平均每小时降雨量是多少英寸？

正确答案 · Correct Answer

解析 · Solution

Solution 1

July has 31 days, or 31×24 hours. Therefore, the average rainfall was

\displaystyle \frac{366}{31×24}

inches per hour.

We can express the number of inches of rain in a ratio,

\displaystyle \frac{366 \text{ inches}}{1\text{ month}}

. We need to find to find the number of hours, but first we need to find the number of days. We know there are 31 days in July, so we get

\displaystyle \frac{366 \text{ inches}}{1 \text{ month}} \times \frac{1 \text{ month}}{31 \text{ days}}

We know there are 24 hours in a day, so we get

\displaystyle \frac{366 \text{ inches}}{1 \text{ month}} \times \frac{1 \text{ month}}{31 \text{ days}} \times \frac{1 \text{ day}}{24 \text{ hours}}

And simplifying gets us

\dfrac{366 \text{ inches}}{31×24 \text{ hours}}

, which is

\text{A}

Note that in the simplifying step, we noted that the month and day units cancel, leaving us with only inches per hour.

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