Difference between revisions of "1980 AHSME Problems/Problem 10"
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== Solution == | == Solution == | ||
| − | <math>\fbox{}</math> | + | 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 == | == See also == | ||
Latest revision as of 14:28, 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:
![\[\frac{k}{x}:\frac{k}{y}:\frac{k}{z}\]](http://latex.artofproblemsolving.com/b/8/9/b89a800203db6d23ec94f810068256e90addee4b.png)
![\[yz:xz:xy.\]](http://latex.artofproblemsolving.com/f/f/d/ffd377a317710b4157f492a6cbebfe4e62908b48.png)
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. 
