2013 AMC 8 第 11 题

Question

特德的祖父本周有

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

小提示：

时间等于距离除以速度

Time equals distance divided by rate.

大提示：

比较实际总时间与以每小时

4

英里的速度走

6

英里所需的时间

Compare the actual total minutes with

6

miles at

4

mph.

视频讲解：

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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，星期一为

\dfrac{2}{5} \cdot 60 = 24

分钟，星期三为

\dfrac{2}{3} \cdot 60 = 40

分钟，星期五为

\dfrac{1}{2} \cdot 60 = 30

分钟。因此实际总时间为

94

分钟。

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

minutes for Monday,

\dfrac{2}{3} \cdot 60 = 40

minutes for Wednesday, and

\dfrac{1}{2} \cdot 60 = 30

minutes for Friday. 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.