119. (Rule XXXI). Two luminaries, being at a given distance ( $d$ ) from each other, move towards each other with given speeds ( $v$ and $v_{1}$ ). Determine the point of their meeting.
119. This problem is, in essence, the progenitor of our notorious "courier problems." Clearly, before the meeting, one celestial body will travel the distance $x$ in $\frac{x}{v}$ time, while the other will travel the distance $d-x$ in $\frac{d-x}{v_{1}}$, hence $\frac{x}{v}=\frac{d-x}{v_{1}}$, from which $x=\frac{v d}{v+v_{1}}$.