1954 AMC 12 Problem 36

Question

A boat has a speed of

15

mph in still water. In a stream that has a current of

5

mph it travels a certain distance downstream and returns. The ratio of the average speed for the round trip to the speed in still water is:

\dfrac54

\dfrac11

\dfrac89

\dfrac78

\dfrac98

The downstream and upstream speeds are

20

mph and

10

mph

For equal distances, divide twice the distance by

\frac{d}{20}+\frac{d}{10}

For a one-way distance

d,

the total time is

\frac d{20}+\frac d{10}=\frac{3d}{20}.

Thus the round-trip average speed is

\frac{2d}{\frac{3d}{20}}=\frac{40}{3}.

Its ratio to

15

is

\frac{\frac{40}{3}}{15}=\frac89.

Thus, the correct answer is C.

Problem 36 in other years