Question

Mia 正在“帮”妈妈把散落在地板上的 $30$ 个玩具捡起来。Mia 的妈妈每 $30$ 秒能把 $3$ 个玩具放进玩具箱，但每次这 $30$ 秒刚结束，Mia 立刻从箱子里拿出 $2$ 个玩具。Mia 和妈妈第一次把全部 $30$ 个玩具放进箱子需要多少分钟？

Mia is "helping" her mom pick up $30$ toys that are strewn on the floor. Mia’s mom manages to put $3$ toys into the toy box every $30$ seconds, but each time immediately after those $30$ seconds have elapsed, Mia takes $2$ toys out of the box. How much time, in minutes, will it take Mia and her mom to put all $30$ toys into the box for the first time?

$13.5$

$14$

$14.5$

$15$

$15.5$

答案：B

知识点：速率过程模拟

难度评级：1140

解答：

每 $30$ 秒妈妈放入 $3$ 个，然后 Mia 拿出 $2$ 个，通常净增加 $+1$ 个。

不过最后阶段要特别注意：妈妈放入玩具后、Mia 拿出玩具前，箱中可能已经第一次达到 $30$ 个。

当箱中已有 $27$ 个玩具时，妈妈再放入 $3$ 个，就有 $30$ 个玩具。

这需要 $27 \cdot 30$ 秒，再加上 $30$ 秒，即分钟，箱中达到 $30$ 个玩具。 $28 \cdot 30 \div 60 = 14$

所以正确答案是 B。

Note that after $30$ seconds, there are $3$ toys added and $2$ removed, leaving a net total of $+1$ toys in the box.

We have to be careful towards the end, however, since it is possible for the box to have $30$ toys right after Mia's mom adds the toys and before Mia removes them.

After there are $27$ toys in the box, Mia's mom can add $3,$ leaving $30$ toys in the box.

It will take $27 \cdot 30$ seconds, plus another $30$ seconds, which gives us $28 \cdot 30 \div 60 = 14$ minutes to get $30$ toys in the box.

Thus, B is the correct answer.

2017 AMC 10A 第 4 题

答案：B

难度评级：1140

解答：

其他年份的第 4 题