Question

Ted 的祖父本周有 $3$ 天使用了跑步机。他每天走或跑 $2$ 英里。

星期一他以每小时 $5$ 英里的速度慢跑。星期三他以每小时 $3$ 英里的速度步行，星期五以每小时 $4$ 英里的速度步行。

如果祖父一直以每小时 $4$ 英里的速度步行，他会少花一些跑步机时间。少多少分钟？

Ted's grandfather used his treadmill on $3$ days this week. He went $2$ miles each day.

On Monday he jogged at a speed of $5$ miles per hour. He walked at the rate of $3$ miles per hour on Wednesday and at $4$ miles per hour on Friday.

If Grandfather had always walked at $4$ miles per hour, he would have spent less time on the treadmill. How many minutes less?

$1$

$2$

$3$

$4$

$5$

答案：D

知识点：路程、速度与时间单位换算

难度评级：1280

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文字解答：

祖父星期一慢跑用时 $\frac{2}{5}$ 小时，星期三步行用时 $\frac{2}{3}$ 小时，星期五用时 $\frac{2}{4}=\frac{1}{2}$ 小时。换算为分钟分别是因此实际总时间为 $94$ 分钟。 $\dfrac{2}{5} \cdot 60 = 24~\mathrm{minutes}$ $\dfrac{2}{3} \cdot 60 = 40~\mathrm{ minutes}$ $\dfrac{1}{2} \cdot 60 = 30~\mathrm{ minutes}$

如果他一直以每小时 $4$ 英里的速度走，每天用时 $\frac{2}{4}=\frac{1}{2}$ 小时，即 $\frac{2}{4} \cdot 60 = 30$ 分钟， $3$ 天共 $3 \cdot 30 = 90$ 分钟。

因此少用的时间是 $94-90=4$ 分钟。

所以正确答案是 D。

Grandfather spent $\frac{2}{5}$ hours jogging on Monday. He spent $\frac{2}{3}$ hours walking on Wednesday and $\frac{2}{4}=\frac{1}{2}$ hours on Friday. Converting these times to minutes, we get $\dfrac{2}{5} \cdot 60 = 24~\mathrm{minutes}$ $\dfrac{2}{3} \cdot 60 = 40~\mathrm{ minutes}$ $\dfrac{1}{2} \cdot 60 = 30~\mathrm{ minutes}$ for Monday, Wednesday, and Friday respectively. Therefore, Grandfather totaled $94$ minutes of exercise throughout the week.

If he walked at a pace of $4$ miles per hour each day, he would have spent $\frac{2}{4}=\frac{1}{2}$ hours each day walking. This equals $\frac{2}{4} \cdot 60 = 30$ minutes every day. If he did this for $3$ days, he would have totaled $3 \cdot 30 = 90$ minutes of exercise.

Therefore, Grandfather would have spent $94-90=4$ fewer minutes on the treadmill.

Thus, D is the correct answer.

2013 AMC 8 第 11 题

答案：D

难度评级：1280

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文字解答：

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