Question 407183
Let s = the stop number where the train fills.

Then 1+2+3+...+s = 78, or

{{{(s(s+1))/2 = 78}}}, or
{{{s^2 + s = 156}}}
{{{s^2 + s - 156 = 0}}}
(s+13)(s-12) = 0
==> s = 12.

Hence on the 12th stop the train is full.