1989 AMC 12 Problem 12

Question

The traffic on a certain east-west highway moves at a constant speed of

60

miles per hour in both directions. An eastbound driver passes

20

westbound vehicles in a five-minute interval. Assume vehicles in the westbound lane are equally spaced. Which of the following is closest to the number of westbound vehicles present in a

100

-mile section of highway?

100

120

200

240

400

Answer: C

Concepts:relative speed distance rate and time ratio and proportion

Difficulty rating: 1360

Small hint:

The cars approach one another at the sum of their speeds

Big hint:

Use the distance covered at relative speed to find the spacing between westbound vehicles

Solution:

The relative speed is

120

miles per hour, so in five minutes the driver covers

10

relative miles. Passing

20

equally spaced vehicles in that distance means the spacing is about

\frac{10}{20}=\frac{1}{2}

mile. Thus a

100

-mile section contains about

\frac{100}{\frac{1}{2}}=200

vehicles.

Thus the correct answer is C.