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Difference between revisions of "1956 AHSME Problems/Problem 45"

(Created page with "A wheel with a rubber tire has an outside diameter of <math>25</math> in. When the radius has been decreased a quarter of an inch, the number of revolutions in one mile will:...")
 
(→‎Solution)
 
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<math>\text{(A)}\ \text{be increased about }2\% \qquad \\ \text{(B)}\ \text{be increased about }1\%  \\ \text{(C)}\ \text{be increased about }20\%\qquad \\ \text{(D)}\ \text{be increased about }\frac{1}{2}\%\qquad \\ \text{(E)}\ \text{remain the same}</math>
 
<math>\text{(A)}\ \text{be increased about }2\% \qquad \\ \text{(B)}\ \text{be increased about }1\%  \\ \text{(C)}\ \text{be increased about }20\%\qquad \\ \text{(D)}\ \text{be increased about }\frac{1}{2}\%\qquad \\ \text{(E)}\ \text{remain the same}</math>
 
==Solution==
 
==Solution==
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The circumference of the normal tire is <math>50\pi</math> inches, while the shaved tire has a circumference of <math>49.5\pi</math> inches. Thus, the ratio of the number of rotations the two tires take to go a mile can be expressed as <math>\frac{5280*12}{50\pi}:\frac{5280*12}{49.5\pi}</math> Simplifying the ratio, we get <math>\frac{1}{100}:\frac{1}{99} \rightarrow 99:100</math>
+
To be added.
  
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The increase in rotations can be expressed as <math>\frac{100-99}{99} \rightarrow \frac{1}{99}</math>. This leads to an increase of <math>\boxed{\textbf{(B) }\text{about } 1\%}</math>
 
 
==See Also==
 
==See Also==
 
Go back to the rest of the [[1956 AHSME Problems]].
 
Go back to the rest of the [[1956 AHSME Problems]].
  
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 20:00, 27 March 2021

A wheel with a rubber tire has an outside diameter of $25$ in. When the radius has been decreased a quarter of an inch, the number of revolutions in one mile will:

$\text{(A)}\ \text{be increased about }2\% \qquad \\ \text{(B)}\ \text{be increased about }1\% \\ \text{(C)}\ \text{be increased about }20\%\qquad \\ \text{(D)}\ \text{be increased about }\frac{1}{2}\%\qquad \\ \text{(E)}\ \text{remain the same}$

Solution

To be added.

See Also

Go back to the rest of the 1956 AHSME Problems.

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