[tex]d_1+d_2=d=50 \ m \\ v_1=6\ m/s \\ v_2=4 \ m/s \\ t_1=t_2=t \\ v=\frac{d}{t} \Rightarrow t=\frac{d}{v} \\ \Rightarrow t_1=\frac{d_1}{v_1}=\frac{d_1}{6 \ m/s} \\ \Rightarrow t_2=\frac{d_2}{v_2}=\frac{50 \ m-d_1}{4 \ m/s} \\ \Rightarrow \frac{d_1}{6}=\frac{50-d_1}{4} \ \Leftrightarrow \ 4d_1=6(50-d_1) \\ 4d_1=300-6d_1 \\ 4d_1+6d_1=300 \ m \\ 10d_1=300 \ m \\ \Rightarrow \boxed{d_1=30 \ m}[/tex]
