1970 AMC 12 第 21 题

Question

一辆汽车去程时，仪表盘显示行驶了

450

英里。装上雪地轮胎后沿同一路线返程，仪表盘显示行驶了

440

英里。若原车轮半径为

15

英寸，求车轮半径增加了多少英寸，精确到百分位。

On an auto trip, the distance read from the instrument panel was

450

miles. With snow tires on for the return trip over the same route, the reading was

440

miles. Find, to the nearest hundredth of an inch, the increase in radius of the wheels if the original radius was

15

inches.

0.33

0.34

0.35

0.38

0.66

实际距离固定时，里程表读数与车轮半径成反比

For a fixed true distance, the odometer reading is inversely proportional to wheel radius

若两个半径为

r_1,r_2

，则利用

450r_1=440r_2

If the radii are

r_1,r_2,

use

450r_1=440r_2

实际距离固定时，里程表读数与车轮转数成正比。因此

450r_1=440r_2, \qquad \frac{r_2}{r_1}=\frac{45}{44}\text{。}

由

r_1=15

可知，增加的半径为

\begin{aligned} r_2-r_1 &=15\left(\frac{45}{44}-1\right)\\ &=\frac{15}{44}\\ &\approx0.3409 \end{aligned}\text{。}

精确到百分位是

0.34

英寸。

因此，正确答案是 B。

For a fixed true distance, the odometer reading is proportional to the number of wheel revolutions. Thus

450r_1=440r_2, \qquad \frac{r_2}{r_1}=\frac{45}{44}.

With

r_1=15,

the increase is

\begin{aligned} r_2-r_1 &=15\left(\frac{45}{44}-1\right)\\ &=\frac{15}{44}\\ &\approx0.3409. \end{aligned}

To the nearest hundredth this is

0.34

inch.

Therefore, the correct answer is B.

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