1958 AMC 12 第 24 题

Question

一个人以每英里

2

分钟的速度向正北行进

m

英尺，再以每分钟

2

英里的速度向正南返回起点。全程的平均速度，以英里每小时计，为：

A man travels

m

feet due north at

2

minutes per mile. He returns due south to his starting point at

2

miles per minute. The average rate in miles per hour for the entire trip is:

75

48

45

24

不知道

m

的值就无法确定

impossible to determine without knowing the value of

m

将两个给定速度都换算成英里每小时

Convert both stated rates to miles per hour

对相等的往返距离，用单程距离的两倍除以两段行程时间之和

For equal distances, divide twice the one-way distance by the sum of the two travel times

北行速度为

30

英里每小时，南行速度为

120

英里每小时。由于往返距离相等，全程平均速度为

\frac{2(30)(120)}{30+120}=48\text{ 英里/小时}\text{。}

距离

m

会约去。

所以正确答案为 B。

The northbound rate is

30

mph, and the southbound rate is

120

mph. For equal distances, the round-trip average is

\frac{2(30)(120)}{30+120}=48\text{ mph}.

The distance

m

cancels.

Therefore, the correct answer is B.

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