Points P and Q are marked on the segment AB, equal to 30m.

Points P and Q are marked on the segment AB, equal to 30m. Find the distance between the midpoints of the segments AQ and PQ, if 3 AP = 2PB and AQ = 2AP

The points are located in the sequence A-P-Q-B.
Let AP = x, then AQ = 2 * x = AP + PQ, therefore, PQ = AP = x, PB = 3/2 * x.
Let’s write the equation:
AP + PQ + QB = 30.
Or, on the other hand (since QB is unknown):
AP + PB = 30,
x + 3/2 * x = 30,
5/2 * x = 30,
X = 12 m.
Therefore, the midpoint of the segment AQ is equal to the segment PQ, and the midpoint of PQ is equal to x / 2 and is equal to 6 m.
Thus, we need to find the distance from point P to the middle of the segment PQ, and it is equal to 6 m.
The distance between the midpoints of segments AQ and PQ is 6 m.