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This is a standard cable/pulley kinematics problem. You need to write the length, L, of the cable in terms of motion parameters for A and P. Let sP represent the distance that P is below the center of the pulley. From this, you can write: L = sP + sqrt(x^2 + h^2) + constant. Setting dL/dt = 0 gives you the relationship between sP_dot and x_dot.
From the animation above, you can see that the speed of crate is never any greater than the speed of the worker, A. Can you see this result in your work?