1952 AHSME Problems/Problem 48

Problem

Two cyclists, $k$ miles apart, and starting at the same time, would be together in $r$ hours if they traveled in the same direction, but would pass each other in $t$ hours if they traveled in opposite directions. The ratio of the speed of the faster cyclist to that of the slower is:

$\text{(A) } \frac {r + t}{r - t} \qquad \text{(B) } \frac {r}{r - t} \qquad \text{(C) } \frac {r + t}{r} \qquad \text{(D) } \frac{r}{t}\qquad \text{(E) } \frac{r+k}{t-k}$

Solution

$[asy] pair A,B,C; A=(0,0); B=(8,0); C=(4,1); draw((A)--(B)); label("$A$",A,S); label("$B$",B,SE); label("$k$",C,SW); [/asy]$

1952 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 47	Followed by Problem 49
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1952 AHSME Problems/Problem 48

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