1. **State the problem:** Hugo walks $\frac{5}{6}$ mile on Monday and $\frac{1}{3}$ mile on Tuesday. We need to find how much farther he walks on Monday than on Tuesday.\n\n2. **Formula used:** To find how much farther, subtract the Tuesday distance from the Monday distance: \n$$\text{Difference} = \text{Monday distance} - \text{Tuesday distance}$$\n\n3. **Calculate the difference:** \n$$\frac{5}{6} - \frac{1}{3}$$\nTo subtract, find a common denominator. The least common denominator of 6 and 3 is 6.\n\n4. **Convert fractions:** \n$$\frac{5}{6} - \frac{\cancel{1} \times 2}{\cancel{3} \times 2} = \frac{5}{6} - \frac{2}{6}$$\n\n5. **Subtract numerators:** \n$$\frac{5 - 2}{6} = \frac{3}{6}$$\n\n6. **Simplify the fraction:** \n$$\frac{\cancel{3} \times 1}{\cancel{6} \times 2} = \frac{1}{2}$$\n\n7. **Answer:** Hugo walks $\frac{1}{2}$ mile farther on Monday than on Tuesday.\n\n8. **Is the answer reasonable?** Yes, because $\frac{5}{6}$ mile is almost one mile, and $\frac{1}{3}$ mile is about one-third of a mile, so the difference being half a mile makes sense.