Question

Roy 的猫每天早上吃 $\dfrac{1}{3}$ 罐猫粮，每天晚上吃 $\dfrac{1}{4}$ 罐猫粮。星期一早上喂猫之前，Roy 打开一个装有 $6$ 罐猫粮的盒子。这只猫在星期几吃完盒子里所有猫粮？

Roy's cat eats $\dfrac{1}{3}$ of a can of cat food every morning and $\dfrac{1}{4}$ of a can of cat food every evening. Before feeding his cat on Monday morning, Roy opened a box containing $6$ cans of cat food. On what day of the week did the cat finish eating all the cat food in the box?

星期二

Tuesday

星期三

Wednesday

星期四

Thursday

星期五

Friday

星期六

Saturday

答案：C

知识点：速率分数日期与时间

难度评级：1140

解答：

这只猫每天吃罐猫粮，所以吃完全部猫粮需要天。这个数介于 $10$ 和 $10\cdot\frac7{12}=\frac{35}{6}$ 之间。 $\frac16$ $\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{7}{12}$

因此它会在第天吃完，也就是星期一之后天。

星期一之后天等同于星期一之后天，也就是星期四。所以正确答案是 C。

The cat eats $\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{7}{12}$ cans of food each full day. After $10$ full days, it has eaten $10\cdot\frac7{12}=\frac{35}{6}$ cans, leaving $\frac16$ of a can.

The cat finishes that remainder during its next morning feeding. The eleventh morning, counting Monday as the first, is Thursday.

Thus, C is the correct answer.

2014 AMC 10A 第 2 题

答案：C

难度评级：1140

解答：

其他年份的第 2 题