Marcus drove from New York toward Chicago at a constant rate of 45 mph. Marie left New York 2 hr. later and drove the same route at 55 mph. How long was Marcus driving before Marie caught up?

Marcus was traveling 11 hours before Marie caught up.

Explanation:

Let the time of travel of Marcus before they caught up be t.

Time of travel of Marie = t - 2

Speed of Marcus = 45 mph

Speed of Marie = 55 mph

Distance traveled by them will be same.

Hence

Speed of Marcus x Time of travel of Marcus before they caught up= Speed of Marie x Time of travel of Marie before they caught up

          45 x t= 55 x (t-2)

          45t= 55 t - 110

           10 t = 110

               t = 11 hours

Marcus was traveling 11 hours before Marie caught up.

You need to be more specific.  i really don't know what a "motion map" is.you can draw a graph of an object's position, distance, displacement, speed,velocity, or acceleration versus time, or you can draw a graph of the object's x-position versus its y-position and not give any information about time at all.if the graph presents position or displacement against time,  then constant velocity is a straight line . . i.e. a line that has  constant slope.if the graph shows speed against time, then constant velocityis a horizontal piece of line.if the graph shows acceleration against time, then constant  velocity is a piece of line that lies on the x-axis . . it's value is zero.