1971 AMC 12 Problem 18

Question

The current in a river flows steadily at

3

miles per hour. A motorboat traveling at a constant rate in still water goes downstream

4

miles and then returns to its starting point. The trip takes one hour, excluding turning time. The ratio of the downstream rate to the upstream rate is:

4:3

3:2

5:3

2:1

5:2

Answer: D

Concepts:relative speed distance rate and time quadratic

Difficulty rating: 1760

Small hint:

Let

v

be the boat’s still-water speed

Big hint:

Solve

\frac{4}{v+3}+\frac{4}{v-3}=1

Solution:

If

v

is the still-water speed, then

\frac4{v+3}+\frac4{v-3}=1.

This simplifies to

v^2-8v-9=0,

so the positive admissible solution is

v=9.

The downstream and upstream rates are

12

and

6,

whose ratio is

2:1.

Therefore, the correct answer is D.