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

Question

Objects R and S each travel at a constant speed. The speed of object R is half the speed of object S. Object R travels a distance of $4 x$ inches in $y$ seconds. Which expression represents the time, in seconds, it takes object S to travel a distance of $24 x$ inches?

A.

$12 y$

B.

$3 y$

C.

$16 y$

D.

$6 y$

Accepted Answer

Choice B is correct. It's given that object R travels a distance of 4 x inches in y seconds. This speed can be written as 4 x &#160; inches y &#160; 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 4 x &#160; inches y &#160; seconds , or 8 x &#160; inches y &#160; seconds . Let n represent the time, in seconds, it takes object S to travel a distance of 24 x inches. The value of n can be found by solving the equation 8 x &#160; inches y &#160; seconds = 24 x &#160; inches n &#160; seconds , which can be written as 8 x y = 24 x n . Multiplying each side of this equation by n y yields 8 x n = 24 x y . Dividing each side of this equation by 8 x yields n = 3 y . Therefore, the expression 3 y represents the time, in seconds, it takes object S to travel a distance of 24 x inches. Choice A is incorrect. This expression represents the time, in seconds, it would take object S to travel a distance of 24 x 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 128 x inches, not 24 x inches. Choice D is incorrect. This expression represents the time, in seconds, it takes object R, not object S, to travel a distance of 24 x inches.

Question object