solution: 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. [asy]
  pair a=(0,1), b=(.75, 0), c=(0,.5), d=(.75,.5), o=(0,0);
  draw(a--b--d--c--cycle);
  label("$A$", a, NW);
  label("$B$", b, SE);
  label("$\frac{1}{2}$", (0,0.75), W);
  label("$\frac{3}{4}$", (.7, 0.66),W);
  label("$\frac{1}{2}$", (.75, .25), E);
  
  picture pic;
  draw(pic, a--b--o--cycle);
  label(pic, "$A$", a, NW);
  label(pic, "$B$", b, SE);
  label(pic, "$\frac{3}{4}$", (.375,0), S);
  label(pic, "1", (0, .5), W);
  add(shift(1.5,0)*pic);
  [/asy] 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 $\boxed{1.25}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Bill walks $\frac{1}{2}$ mile south, then $\frac{3}{4}$ mile east, and finally $\frac{1}{2}$ mile south. How many miles is he, in a direct line, from his starting point?  Express your answer as a decimal to the nearest hundredth.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 1.25
extra_info.question: Bill walks $\frac{1}{2}$ mile south, then $\frac{3}{4}$ mile east, and finally $\frac{1}{2}$ mile south. How many miles is he, in a direct line, from his starting point?  Express your answer as a decimal to the nearest hundredth.
extra_info.split: test