Objects R and S each travel at a constant speed. The speed of object R is

Choice B is correct. It's given that object R travels a distance of $4x$ inches in $y$ seconds. This speed can be written as $\frac{4x \text{inches}}{y \text{seconds}}$. It's given that the speed of object R is half the speed of object S. It follows that the speed of object S is twice the speed of object R, which is $2\left(\frac{4x \text{inches}}{y \text{seconds}}\right)$, or $\frac{8x \text{inches}}{y \text{seconds}}$. Let $n$ represent the time, in seconds, it takes object S to travel a distance of $24x$ inches. The value of $n$ can be found by solving the equation $\frac{8x \text{inches}}{y \text{seconds}}=\frac{24x \text{inches}}{n \text{seconds}}$, which can be written as $\frac{8x}{y}=\frac{24x}{n}$. Multiplying each side of this equation by $ny$ yields $8xn=24xy$. Dividing each side of this equation by $8x$ yields $n=3y$. Therefore, the expression $3y$ represents the time, in seconds, it takes object S to travel a distance of $24x$ inches.

Choice A is incorrect. This expression represents the time, in seconds, it would take object S to travel a distance of $24x$ inches if the speed of object R were twice, not half, the speed of object S.

Choice C is incorrect. This expression represents the time, in seconds, it takes object S to travel a distance of $128x$ inches, not $24x$ inches.

Choice D is incorrect. This expression represents the time, in seconds, it takes object R, not object S, to travel a distance of $24x$ inches.