1952 AMC 12 Problem 32

Question

K

takes

30

minutes less time than

M

to travel a distance of

30

miles.

K

travels

\dfrac13

mile per hour faster than

M.

If

x

is

K

’s rate of speed in miles per hour, then

K

’s time for the distance is:

\dfrac{x+\frac{1}{3}}{30}

\dfrac{x-\frac{1}{3}}{30}

\dfrac{30}{x+\frac{1}{3}}

\dfrac{30}{x}

\dfrac{x}{30}

Use the basic relation

\text{time}=\frac{\text{distance}}{\text{rate}}

The question asks only for

K

’s time, and both

K

’s distance and rate are already given

For

K,

the distance is

30

miles and the rate is

x

miles per hour. Thus

\text{time}=\frac{\text{distance}}{\text{rate}} =\frac{30}{x}\text{ hours}.

The comparison with

M

is not needed for this expression.

Thus, the correct answer is D.

Problem 32 in other years