Point $C$ is the midpoint of $\overline{AB}$, point $D$ is the midpoint of $\overline{AC}$, point $E$ is the midpoint of $\overline{AD}$, and point $F$ is the midpoint of $\overline{AE}$. If $AF=3$, what is the number of units in the length of $\overline{AB}$?
I need to find the length of $\overline{AB}$, which is twice the length of $\overline{AC}$, which is twice the length of $\overline{AD}$, which is twice the length of $\overline{AE}$, which is twice the length of $\overline{AF}$. So, $\overline{AB} = 2 \cdot \overline{AC} = 4 \cdot \overline{AD} = 8 \cdot \overline{AE} = 16 \cdot \overline{AF}$. Since $\overline{AF} = 3$, I can plug that in and get $\overline{AB} = 16 \cdot 3 = 48$. 