2008 AMC 10A 第 13 题

Question

Doug 粉刷一个房间需要

5

小时。Dave 粉刷同一个房间需要

7

小时。Doug 和 Dave 一起粉刷这个房间，并午餐休息一小时。设

t

为他们一起完成工作所需的总时间（小时），包括午餐。

t

满足下列哪个方程？

Doug can paint a room in

5

hours. Dave can paint the same room in

7

hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let

t

be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by

t?

\left(\dfrac{1}{5} + \dfrac{1}{7}\right)(t + 1) = 1

\left(\dfrac{1}{5} + \dfrac{1}{7}\right)t + 1 = 1

\left(\dfrac{1}{5} + \dfrac{1}{7}\right)t = 1

\left(\dfrac{1}{5} + \dfrac{1}{7}\right)(t - 1) = 1

(5 + 7)t = 1

答案：D

知识点：速率一次方程

难度评级：1280

小提示：

他们一起每工作一小时粉刷

\dfrac{1}{5} + \dfrac{1}{7}

个房间。

Together they paint

\dfrac{1}{5} + \dfrac{1}{7}

of the room each working hour

大提示：

因为午餐休息一小时，他们实际工作

t - 1

小时。

They actually work for

t - 1

hours because of the one-hour lunch break

解答：

Doug 和 Dave 一起每小时粉刷

\dfrac{1}{5} + \dfrac{1}{7}

个房间。

由于休息一小时，他们实际只工作

t - 1

小时，而这段时间必须完成整个房间：

\left(\dfrac{1}{5} + \dfrac{1}{7}\right)(t - 1) = 1\text{。}

所以正确答案是 D。

Working together, Doug and Dave paint

\dfrac{1}{5} + \dfrac{1}{7}

of the room per hour.

Because they break for one hour, they work for only

t - 1

hours, and this must complete the whole room:

\left(\dfrac{1}{5} + \dfrac{1}{7}\right)(t - 1) = 1.

Thus, the correct answer is D.

2008 AMC 10A 第 13 题

答案：D

难度评级：1280

小提示：

大提示：

解答：

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