Question

一杯沸水（ $212^\circ$ F）放在一个温度保持 $68^\circ$ F 的房间中冷却。假设水温与室温的差每 $5$ 分钟减半。 $15$ 分钟后，水温是多少华氏度？

A cup of boiling water ( $212^\circ$ F) is placed to cool in a room whose temperature remains constant at $68^\circ$ 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?

$77$

$86$

$92$

$98$

$104$

答案：B

知识点：等比数列

难度评级：900

解答：

当前水温和室温的差为 $212-68 = 144$ 。

$15$ 分钟包含三个 $5$ 分钟，所以温差会减半 $3$ 次。

也就是说温差乘以 $(\dfrac{1}{2})^3 = \dfrac{1}{8}$ ，新的温差是 $\dfrac{1}{8}\cdot144=18$ 。水温为 $68+18=86$ 。

正确答案是 B。

The current difference is $212-68 = 144 .$

Since we have $15$ minutes while halving every $5$ minutes, we halve the difference $3$ times.

This means the difference is multiplied by $(\dfrac{1}{2})^3 = \dfrac{1}{8} ,$ so our new difference is $\dfrac{1}{8}\cdot144=18.$ This makes our final temperature $68+18=86.$

Thus, the correct answer is B.

2022 AMC 8 第 9 题

答案：B

难度评级：900

解答：

其他年份的第 9 题