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Difference between revisions of "1966 AHSME Problems/Problem 34"

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== Solution ==
 
== Solution ==
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<math>The circumference of the wheel is </math>\frac{11}{5280}<math> miles. Let the time for the rotation in seconds be </math>t<math>. So </math>rt=\frac{11}{5280}*3600<math>. We also know reducing the time by </math>\frac{1}{4}<math> of a second makes </math>r<math> increase by </math>5<math>. So </math>(r+5)(t-\frac{1}{4})=\frac{11}{5280}*3600<math>. Solving for </math>r<math> we get </math>r=10<math>. So our answer is </math>(B)<math> </math>10<math>.</math>
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The circumference of the wheel is <math>\frac{11}{5280}</math> miles. Let the time for the rotation in seconds be <math>t</math>. So <math>rt=\frac{11}{5280}*3600</math>. We also know reducing the time by <math>\frac{1}{4}</math> of a second makes <math>r</math> increase by <math>5</math>. So <math>(r+5)(t-\frac{1}{4})=\frac{11}{5280}*3600</math>. Solving for <math>r</math> we get <math>r=10</math>. So our answer is <math>(B)</math> <math>10</math>.
  
 
== See also ==
 
== See also ==
 
{{AHSME box|year=1966|num-b=33|num-a=35}}   
 
{{AHSME box|year=1966|num-b=33|num-a=35}}   
  
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[[Category:Intermediate Algebra Problems]]
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[[Category:Introductory Algebra Problems]]
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 18:59, 29 May 2024

Problem

Let $r$ be the speed in miles per hour at which a wheel, $11$ feet in circumference, travels. If the time for a complete rotation of the wheel is shortened by $\frac{1}{4}$ of a second, the speed $r$ is increased by $5$ miles per hour. Then $r$ is:

$\text{(A) } 9 \quad \text{(B) } 10 \quad \text{(C) } 10\frac{1}{2} \quad \text{(D) } 11 \quad \text{(E) } 12$

Solution

The circumference of the wheel is $\frac{11}{5280}$ miles. Let the time for the rotation in seconds be $t$. So $rt=\frac{11}{5280}*3600$. We also know reducing the time by $\frac{1}{4}$ of a second makes $r$ increase by $5$. So $(r+5)(t-\frac{1}{4})=\frac{11}{5280}*3600$. Solving for $r$ we get $r=10$. So our answer is $(B)$ $10$.

See also

1966 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 33 		Followed by
Problem 35
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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