AHSME 1952 Problem 48

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