2001 AMC 8 第 15 题

先试着解答 2001 AMC 8 第 15 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2001 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

15.

荷马开始以每分钟削 33 个土豆的速度削一堆 4444 个土豆。四分钟后克里斯滕加入,以每分钟削 55 个土豆的速度削。完成时,克里斯滕削了多少个土豆?
Homer began peeling a pile of 4444 potatoes at the rate of 33 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 55 potatoes per minute. When they finished, how many potatoes had Christen peeled?
2020
2424
3232
3333
4040
答案:A
知识点:速率
小提示:
先求克里斯滕开始时还剩多少个土豆
Find how many potatoes remain when Christen starts
大提示:
之后他们合起来每分钟削 88 个
After that, their combined rate is 88 per minute
解答:
克里斯滕加入时,荷马已经削了 3⋅4=123 \cdot 4 = 12 个土豆,还剩 44−12=3244 - 12 = 32 个。
荷马和克里斯滕合起来每分钟削 5+3=85 + 3 = 8 个土豆,因此还需要 32÷8=432 \div 8 = 4 分钟削完剩下的。
44 分钟内,克里斯滕削了 4⋅5=204 \cdot 5 = 20 个土豆。
所以正确答案是 A。
Homer had peeled 3⋅4=123 \cdot 4 = 12 potatoes by the time Christen joined him, leaving 44−12=3244 - 12 = 32 potatoes.
Together, Homer and Christen peel 5+3=85 + 3 = 8 potatoes per minute, taking them 32÷8=432 \div 8 = 4 minutes to peel the rest.
In 44 minutes, Christen peeled 4⋅5=204 \cdot 5 = 20 potatoes.
Thus, A is the correct answer.
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