We can start by drawing the segment:
We know that AP is 3/8 of the distance AB.
We then know that:
[tex]PB=AB-AP=AB-\frac{3}{8}AB=(1-\frac{3}{8})AB=\frac{5}{8}AB[/tex]Then, the ratio between the two segments become:
[tex]\frac{AP}{PB}=\frac{\frac{3}{8}AB}{\frac{5}{8}AB}=\frac{3}{8}\cdot\frac{8}{5}=\frac{3}{5}[/tex]The ratio AP/PB is 3/5.
(If we express this as PB/AP the ratio would be 5/3).
