On a number line, the coordinates of $P$ and $Q$ are 8 and 48, respectively. The midpoint of $\overline{PQ}$ is $B$, the midpoint of $\overline{BQ}$ is $C$, and the midpoint of $\overline{PC}$ is $D$. What is the coordinate of $D$?
Since $B$ is midpoint of $\overline{PQ}$, the coordinate of $B$ is $(8+48)/2 = 4+24 = 28$.  Since $C$ is the midpoint of $\overline{BQ}$, the coordinate of $C$ is $(28+48)/2 = 14+24=38$.  Since $D$ is the midpoint of $\overline{PC}$, the coordinate of $D$ is $(8+38)/2 = 4 + 19 = \boxed{23}$.

[asy]
pair P, Q, B, C, D;

P = (8,0);
Q = (48,0);
B = (P+Q)/2;
C = (B+Q)/2;
D = (P+C)/2;

dot(P);
dot(Q);
dot(B);
dot(C);
dot(D);

draw(P--Q);
label("$P$",P,S);
label("$Q$",Q,S);
label("$B$",B,S);
label("$C$",C,S);
label("$D$",D,S);
[/asy]