1973 AHSME Problems/Problem 29

Problem

Two boys start moving from the same point A on a circular track but in opposite directions. Their speeds are 5 ft. per second and 9 ft. per second. If they start at the same time and finish when they first me at the point A again, then the number of times they meet, excluding the start and finish, is

$\textbf{(A)}\ 13 \qquad \textbf{(B)}\ 25 \qquad \textbf{(C)}\ 44 \qquad \textbf{(D)}\ \text{infinity} \qquad \textbf{(E)}\ \text{none of these}$

Solution (WIP)

Let $d$ be the length of the track in feet and $x$ be the number of laps that one of the boys did, so time one of the boys traveled before the two finish is $\frac{dx}{5}$ . Since the time elapsed for both boys is equal, one boy ran $5(\frac{dx}{5})$ feet while the other boy ran $9(\frac{dx}{5})$ feet.

1973 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 28	Followed by Problem 30
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1973 AHSME Problems/Problem 29

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Solution (WIP)

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