Difference between revisions of "1980 AHSME Problems/Problem 10"
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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> | ||
+ | |||
+ | == Solution == | ||
+ | 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: | ||
+ | <cmath>\frac{k}{x}:\frac{k}{y}:\frac{k}{z}</cmath> | ||
+ | <cmath>yz:xz:xy.</cmath> | ||
+ | Therefore, the answer is <math>\fbox{D: yz:xz:xy}</math>. | ||
+ | |||
+ | == See also == | ||
+ | {{AHSME box|year=1980|num-b=9|num-a=11}} | ||
+ | |||
+ | [[Category: Introductory Algebra Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 15:28, 22 April 2016
Problem
The number of teeth in three meshed gears ,
, and
are
,
, and
, respectively. (The teeth on all gears are the same size and regularly spaced.) The angular speeds, in revolutions per minutes of
,
, and
are in the proportion
Solution
The distance that each of the gears rotate is constant. Let us have the number of teeth per minute equal to . The revolutions per minute are in ratio of:
Therefore, the answer is
.
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.