I have another question that stumped me

Question

Line segment AB with length a is divided by points P and Q into three line segments: AP , PQ, and QB , such that AP = 2PQ=2QB. Find:
A)the distance between point A and the midpoints of the segments the segment QB
B) the distance between the midpoints of segments AP and QB.

I don't get what this question wants from me can you please describe the proces and the steps for this question
Thanks
:)

Answer 1

You know that

AP+PQ+QB = a

Now, AP = 2PQ = 2BQ
That means that PQ = QB and that gives us

2PQ + PQ + PQ = a
4PQ = a
PQ = a/4

Let M be the midpoint of QB
Let N be the midpoint of AP
AM = AP+PQ+ QB/2
= a/2 + a/4 + a/8 = 7a/8
NM = AP/2 + PQ + QB/2
= a/4 +a/4 + a/8 = 5a/8

Draw and label the line segment AB and you can see this is true.

Answer 2

a. 7/8 a
b. 5a/8
checked on math program and says correct :))