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Difference between revisions of "1980 AHSME Problems/Problem 10"

(Created page with "==Problem== The number of teeth in three meshed gears <math>A</math>, <math>B</math>, and <math>C</math> are <math>x</math>, <math>y</math>, and <math>z</math>, respectively. (T...")
 
(→‎Solution)
 
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<math>\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</math>
 
<math>\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</math>
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== Solution ==
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The distance that each of the gears rotate is constant. Let us have the number of teeth per minute equal to <math>k</math>. The revolutions per minute are in ratio of:
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<cmath>\frac{k}{x}:\frac{k}{y}:\frac{k}{z}</cmath>
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<cmath>yz:xz:xy.</cmath>
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Therefore, the answer is <math>\fbox{D: yz:xz:xy}</math>.
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== See also ==
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{{AHSME box|year=1980|num-b=9|num-a=11}} 
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[[Category: Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 14:28, 22 April 2016

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

See also

1980 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 9 		Followed by
Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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