Constrained motion kinematics

Consider the situation of a person, A, walking to the right with a constant speed. As they walk, they hold a rope that is used to lift a crate P.

As the person walks, take note of the speed of the crate. Although the person is walking with a constant speed, the speed of the crate is NOT constant. In fact, we see that the speed of the crate continues to increase as the person walks, however, this speed never exceeds that of the person.

Can you see physically why the speed of the crate increases, and that it is always less than the speed of the person? Do the kinematic analysis on this problem - can you see from your math why the above statements are true?