Ada and Luisa train every day, each always at the same speed, for the big race that will take place at the end of the year at school. The training starts at point $A$ and ends at point $B$, which are $3000 \mathrm{~m}$ apart. They start at the same time, but when Luisa finishes the race, Ada still has $120 \mathrm{~m}$ to go to reach point $B$. Yesterday, Luisa gave Ada a chance: "We start at the same time, but I start a few meters before point A so we can finish together." How many meters before point $A$ should Luisa start to finish together with Ada?
We know that speed is the ratio of the distance traveled to the time spent. Since the speeds of Luisa and Ada are constant, the distance traveled by each is proportional to the time elapsed. Therefore, if Ada travels $3000-120=2880 \mathrm{~m}$ in the same time that Luisa travels $3000 \mathrm{~m}$, then Ada will travel $3000 \mathrm{~m}$ in the same time that Luisa travels $d \mathrm{~m}$, in a direct proportion.

$$
\begin{array}{rlc}
\text { Luisa } & \rightarrow \text { Ada } \\
3000 & \rightarrow 2880 \\
d & \rightarrow 3000
\end{array}
$$

Thus, $d=\frac{3000^{2}}{2880}=3125$ and Luisa should start $125 \mathrm{~m}$ before point A to arrive at point $\mathrm{B}$ together with Ada.