B will catch up to A when they have both gone the same distance
past the station. So, if we get expressions for both of their
Distances, we can set those equal to each other for our
equation. B's rate was 120 and we do not know it's time, so we
call that x. Since D = RT, that makes D for this train 120x.A's
rate was 100 and we do not know it's time, but we do know that
it had a .25 hour (15 minutes is .25 hours) head start on B.
Since we called B's time x, we can then call A's time (x + .25).
D = RT, so A's D is going to be 100(x + .25). Now we set both of
these expressions for our D's equal to each other for our
equation.120x = 100(x + .25)Distribute the 100.120x = 100x +
25Subtract 100x from both sides.20x = 25Divide both sides by
20.x = 1.25So, B will catch up to A after 1.25 hours. What time
will that be? Well, 1.25 hours is 1 hour and 15 minutes. Add
that to the starting time of 1:25 and we get that B catches up
at 2:40.