jmc

The diagram on the left shows the path of Bill's walk. As the diagram on the right illustrates, he could also have walked from $A$ to $B$ by first walking 1 mile south then $\frac{3}{4}$ mile east. By the Pythagorean Theorem, $$(AB{)}^2=1^2+{\left(\frac{3}{4}\right)}^2=1+\frac{9}{16}=\frac{25}{16},$$so $AB=\frac{5}{4}=1\frac{1}{4}$, or $\boxed{1.25}$.