Let us consider the initial position of train A, [tex]s_{0A}=0[/tex]. This implies that [tex]s_{0B}=500[/tex].
Moreover, we have
[tex]v_A=150, \quad v_B=-100[/tex]
This implies that the two equations are
[tex]s_A(t)=150t,\quad s_B(t)=500-100t[/tex]
The two trains meet if and only if their positions are the same, at the same time:
[tex]s_A(t)=s_B(t) \iff 150t=500-100t \iff 250t=500 \iff t=2[/tex]
So, the two trains meet after 2 hours.
