Difference between revisions of "1951 AHSME Problems/Problem 28"
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| − | + | Because <math>P</math> varies jointly as <math>A</math> and <math>V^2</math>, that means that there is a number <math>k</math> such that <math>P=kAV^2</math>. You are given that <math>P=1</math> when <math>A=1</math> and <math>V=16</math>. That means that <math>1=k(1)(16^2) \rightarrow k=\frac{1}{256}</math>. Then, substituting into the original equation with <math>P=36</math> and <math>A=9</math> (because a square yard is <math>9</math> times a square foot), you get <math>4=\frac{1}{256}(V^2)</math>. Solving for <math>V</math>, we get <math>V^2=1024</math>, so <math>V=32</math>, and hence the answer is <math>\boxed{C}</math>. | |
== See Also == | == See Also == | ||
{{AHSME 50p box|year=1951|num-b=27|num-a=29}} | {{AHSME 50p box|year=1951|num-b=27|num-a=29}} | ||
Revision as of 18:43, 20 November 2014
Problem
The pressure 
of wind on a sail varies jointly as the area 
of the sail and the square of the velocity 
of the wind. The pressure on a square foot is 
pound when the velocity is 
miles per hour. The velocity of the wind when the pressure on a square yard is 
pounds is:
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Because 
varies jointly as 
and 
, that means that there is a number 
such that 
. You are given that 
when 
and 
. That means that 
. Then, substituting into the original equation with 
and 
(because a square yard is 
times a square foot), you get 
. Solving for 
, we get 
, so 
, and hence the answer is 
.
See Also
| 1951 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 27 |
Followed by Problem 29 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
