Maya walked a part of her journey. She travelled 40 3/4 km by bus and 5 1/2 km by motorcycle. Her total journey was 47 3/4 km. How far did Maya walk?

Step 1: Write down the given distances.
Distance by bus $= 40 \frac{3}{4}$ km
Distance by motorcycle $= 5 \frac{1}{2}$ km
Total journey distance $= 47 \frac{3}{4}$ km

Step 2: Convert all mixed numbers to improper fractions.

$$40 \frac{3}{4} = \frac{(40 \times 4) + 3}{4} = \frac{160 + 3}{4} = \frac{163}{4}$$ $$5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}$$ $$47 \frac{3}{4} = \frac{(47 \times 4) + 3}{4} = \frac{188 + 3}{4} = \frac{191}{4}$$

Step 3: Calculate the total distance covered by bus and motorcycle.
To add $\frac{163}{4}$ and $\frac{11}{2}$, find a common denominator, which is 4.

$$\frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4}$$

Distance by bus and motorcycle $= \frac{163}{4} + \frac{22}{4} = \frac{163 + 22}{4} = \frac{185}{4} \text{ km}$$

Step 4: Subtract the combined distance from the total journey distance to find the distance walked.
Distance walked $= \text{Total journey distance} - \text{Distance by bus and motorcycle}$

$$= \frac{191}{4} - \frac{185}{4}$$ $$= \frac{191 - 185}{4}$$ $$= \frac{6}{4}$$

Step 5: Simplify the fraction and convert it back to a mixed number.

$$\frac{6}{4} = \frac{3}{2} = 1 \frac{1}{2} \text{ km}$$

The distance Maya walked was $\boxed{1 \frac{1}{2} \text{ km}}$.