Difference between revisions of "1959 AHSME Problems/Problem 30"

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== Solution ==
 
== Solution ==
  
In <math>15</math> seconds, A will complete <math>\frac{3}{8}</math> of the track. This means that B will complete <math>\frac{5}{8}</math> of the track in <math>15</math> seconds, meaning that to complete the whole track (making the fraction 1), it will take <math>\frac{8}{5} \cdot 15 = 24</math> seconds. So the answer is <math>\boxed{B}</math>.
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In <math>15</math> seconds, A will complete <math>\frac{3}{8}</math> of the track. This means that B will complete <math>\frac{5}{8}</math> of the track in <math>15</math> seconds, meaning that to complete the whole track (making the fraction 1), it will take <math>\frac{8}{5} \cdot 15 = 24</math> seconds. So the answer is <math>\boxed{\textbf{(B) }24}</math>.
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== See also ==
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{{AHSME 50p box|year=1959|num-b=29|num-a=31}}
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{{MAA Notice}}
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[[Category:Introductory Algebra Problems]]

Latest revision as of 14:33, 21 July 2024

Problem

$A$ can run around a circular track in $40$ seconds. $B$, running in the opposite direction, meets $A$ every $15$ seconds. What is $B$'s time to run around the track, expressed in seconds? $\textbf{(A)}\ 12\frac12 \qquad\textbf{(B)}\ 24\qquad\textbf{(C)}\ 25\qquad\textbf{(D)}\ 27\frac12\qquad\textbf{(E)}\ 55$

Solution

In $15$ seconds, A will complete $\frac{3}{8}$ of the track. This means that B will complete $\frac{5}{8}$ of the track in $15$ seconds, meaning that to complete the whole track (making the fraction 1), it will take $\frac{8}{5} \cdot 15 = 24$ seconds. So the answer is $\boxed{\textbf{(B) }24}$.

See also

1959 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 29
Followed by
Problem 31
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All AHSME Problems and Solutions

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