Question 128001
I put a stopwatch on the 2 trains, but I wait until the moment
the 2nd train leaves. How far has the 1st train gone at that
point? {{{50*3 = 150}}} miles
Let {{{t}}} = elapsed time starting when 2nd train leaves
Let {{{d}}} = distance the 1st train has to travel to the point
where they meet
Then {{{d + 150}}} is the distance the 2nd train has to travel 
to get to their meeting point
{{{d = 50t}}}
{{{d + 150 = 65t}}}
Substitute {{{d}}} in the 1st equation for {{{d}}} in the 2nd 
{{{50t + 150 = 65t}}}
{{{15t = 150}}}
{{{t = 10}}} hrs
It will take the 2nd train 10 hours to overtake the 1st train
check:
{{{d = 50t}}}
{{{d + 150 = 65t}}}
-------------------
{{{d = 50*10}}}
{{{d = 500}}} mi
-------------------
{{{d + 150 = 65t}}}
{{{d = 65*10 - 150}}}
{{{d = 500}}} mi
OK