AMC 8 2022 Problem 9

AMC8 2022 年第 9 题

数列与规律★★☆☆☆

A cup of boiling water (

212^{\circ}\text{F}

) is placed to cool in a room whose temperature remains constant at

68^{\circ}\text{F}

. Suppose the difference between the water temperature and the room temperature is halved every 5 minutes. What is the water temperature, in degrees Fahrenheit, after 15 minutes?

一杯开水（212 华氏度）被放置在一个温度恒定为 68 华氏度的房间里进行冷却。假设水的温度和房间温度的差值每 5 分钟减半。问在 15 分钟后，水的温度是多少华氏度？

A.77
B.86
C.92
D.98
E.104

正确答案 · Correct Answer

解析 · Solution

Solution 1

Initially, the difference between the water temperature and the room temperature is 212-68=144 degrees Fahrenheit. After 5 minutes, the difference between the temperatures is

144\div2=72

degrees Fahrenheit. After 10 minutes, the difference between the temperatures is

72\div2=36

degrees Fahrenheit. After 15 minutes, the difference between the temperatures is

36\div2=18

degrees Fahrenheit. At this point, the water temperature is 68+18=86 degrees Fahrenheit.

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