1970 AMC 12 Problem 21

Question

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

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

If the radii are

r_1,r_2,

use

450r_1=440r_2

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.

Problem 21 in other years