The number of teeth in three meshed gears $A$, $B$, and $C$ are $x$, $y$, and $z$, respectively. (The teeth on all gears are the same size and regularly spaced.) The angular speeds, in revolutions per minutes of $A$, $B$, and $C$ are in the proportion
$\text{(A)} \ x: y: z ~~\text{(B)} \ z: y: x ~~ \text{(C)} \ y: z: x~~ \text{(D)} \ yz: xz: xy ~~ \text{(E)} \ xz: yx: zy$
The distance that each of the gears rotate is constant. Let us have the number of teeth per minute equal to $k$. The revolutions per minute are in ratio of:
\[\frac{k}{x}:\frac{k}{y}:\frac{k}{z}\]
\[yz:xz:xy.\]
Therefore, the answer is $\fbox{D: yz:xz:xy}$.