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:

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

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

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

$\dfrac{30}{x}$

$\dfrac{x}{30}$

Answer: D

Concepts:distance rate and time rate

Difficulty rating: 920

Small Hint:

Use the basic relation $\text{time}=\frac{\text{distance}}{\text{rate}}$

Big Hint:

The question asks only for $K$ ’s time, and both $K$ ’s distance and rate are already given

Solution:

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.

1952 AMC 12 Problem 32

Answer: D

Difficulty rating: 920

Small Hint:

Big Hint:

Solution:

Problem 32 in Other Years