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

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：

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

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

解答：

其他年份的第 13 题