Answer :
Answer:
The trains will meet 225km north from the station.
Explanation:
First, we need the equation of position of the two trains. Since they have constant velocities, these equations are:
[tex]x_1=v_1(t+t_0)\\\\x_2=v_2t}[/tex]
Where [tex]t_0[/tex] is the time the first train is traveling before the second train levaes the station. When the trains meet, [tex]x_1=x_2=x[/tex] . If we solve for t in the equations above, we have:
[tex]t=\frac{x}{v_1}-t_0\\ \\t=\frac{x}{v_2}[/tex]
Matching these equations and solving for x, we obtain:
[tex]\frac{x}{v_1}-t_0=\frac{x}{v_2}\\\\xv_2-v_1v_2t_0=xv_1\\\\x(v_2-v_1)=v_1v_2t_0\\\\x=\frac{v_1v_2t_0}{v_2-v_1}\\ \\\implies x=\frac{(45km/h)(75km/h)(2h)}{75km/h-45km/h}=225km[/tex]
In words, the trains will meet 225km north from the station.