1980 AHSME Problems/Problem 10

Problem

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

$\text{(A)} \ x: y: z ~~\text{(B)} \ z: y: x ~~ \text{(C)} \ y: z: x~~ \text{(D)} \ yz: xz: xy ~~ \text{(E)} \ xz: yx: zy$

Solution

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 $\fbox{D: yz:xz:xy}$ .

1980 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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1980 AHSME Problems/Problem 10

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