SOLUTION: A person sets out from Boston and walks toward Portland at the rate of3.0km/h . Three hours afterward, a second person sets out from the same place and walks in the same direction

Let t be the time (in hours) counted from the moment the second person started from Boston to the the overtaking moment.

Then the distance covered by the second person is his rate multiplied by time:

d = 4*t.        (1)

For the first person his time from his start to the overtaking moment is (t+3) hours.
Therefore, the distance covered by the first person during this time is
d = 3*(t+3).    (2)

The distance (1) and (2) is actually the same (!).  It is the key moment in the solution (!!)

Therefore, you have an equation

4t = 3(t+3).

Simplify and solve it for t:

4t = 3t + 9,  or

4t - 3t = 9,

t = 9.

So, you found that the second person will overtake the first one after 9 hours after the second person start.

During this time, the second person vill cover 9*6 = 36 kilometers.

Thus the overtaking point is 36 kilometers apart Boston.

When the second started, the first was just in 3*3 = 9 km from the starting point.

The distance between them decrease 1 kilometer per each hour: 1 = 4 - 3 (!).

So, it will take 9 hours for the second to catch the first.

In 9 hours, the second will cover 4*9 = kilometers (!).

The same answer (!!).

The "true" physicist, or, in general, an advanced person writes momentarily

     t =  = 9 hours for the second to catch the first.

     d = 9*4 = 36 kilometers (the distance)

and everything is clear to him without any explanations.

It is the level you should to strive for.