29. As shown in the figure, it is known that the numbers corresponding to points $A, B, C, D$ on the number line are $-800, -400, 0, 200$. Moving points $P, Q$ start from points $A, C$ respectively at the same time, both moving to the left, with point $P$ moving at a speed of 10 units per second and point $Q$ moving at a speed of 5 units per second. Point $M$ is the midpoint of segment $PQ$. During the entire movement process, the value of $\frac{1}{k} \cdot QD - BM$ remains constant, then the value of $k$ is $\qquad$. (The result should be expressed as a simplified fraction)
$\frac{2}{3}$