Problem (Algebra):
Let $S=15$ and let $M=10$ . Sam and Marty each ride a bicycle at a constant speed. Sam's speed is $S \mathrm{~km} / \mathrm{hr}$ and Marty's speed is $M \mathrm{~km} / \mathrm{hr}$. Given that Sam and Marty are initially $100 \mathrm{~km}$ apart and they begin riding towards one another at the same time, along a straight path, compute the number of kilometers that Sam will have traveled when Sam and Marty meet.

Solution:
In km/hr, the combined speed of Sam and Marty is $S+M$. Thus one can determine the total time they traveled and use this to determine the number of kilometers that Sam traveled. However, this is not needed, and there is a simpler approach. Suppose that Marty traveled a distance of $d$. Then because Sam's speed is $\frac{S}{M}$ of Marty's speed, Sam will have traveled a distance of $\frac{S}{M} \cdot d$. Thus, together, they traveled $d+\frac{S}{M} \cdot d$. Setting this equal to 100 and solving yields $d=\frac{100 M}{M+S}$. Thus Sam traveled $\frac{S}{M} \cdot d=\frac{100 S}{M+S}$. With $S=15$ and $M=10$, this is equal to $60 \mathrm{~km}$.

Final answer: 60