Calculate the sanitation costs for properties in Johannesburg and Cape Town based on given tariffs and usage.

The property area is $175 \text{ m}^2$.

For Johannesburg, properties "Up to and including $300 \text{ m}^2$" have a sanitation cost.

The cost is R228,06.

The cost for sanitation in Johannesburg for a $175 \text{ m}^2$ property is $\boxed{\text{R}228,10}$.

The usage is $4,1 \text{ k}\ell$. This falls into the "0-4,2 kℓ" band.

The current tariff for this band is R16,03 per kℓ. The increase from previous is R0,66 per kℓ.

The cost for $4,1 \text{ k}\ell$ sanitation in Cape Town before the increase is $\boxed{\text{R}63,02}$.

Jones's sanitation cost (Johannesburg).
Mr. Jones's property area is $550 \text{ m}^2$. According to the Johannesburg table, this falls into the "Larger than $300 \text{ m}^2$ to $1\,000 \text{ m}^2$" category. The cost is fixed based on property area.

Brown's sanitation cost (Cape Town).
Ms. Brown's sanitation usage is $22 \text{ k}\ell$. Cape Town uses a stepped tariff system based on usage.

• For the first $4,2 \text{ k}\ell$ (0-4,2 kℓ band) at R16,03 per kℓ: $$4,2 \text{ k}\ell \times \text{R}16,03/\text{k}\ell = \text{R}67,326$$
• For the next $3,15 \text{ k}\ell$ (from 4,2 kℓ to 7,35 kℓ) at R22,02 per kℓ: $$(7,35 - 4,2) \text{ k}\ell \times \text{R}22,02/\text{k}\ell = 3,15 \text{ k}\ell \times \text{R}22,02/\text{k}\ell = \text{R}69,363$$
• For the remaining $14,65 \text{ k}\ell$ (from 7,35 kℓ to 22 kℓ) at R30,92 per kℓ: $$(22 - 7,35) \text{ k}\ell \times \text{R}30,92/\text{k}\ell = 14,65 \text{ k}\ell \times \text{R}30,92/\text{k}\ell = \text{R}453,008$$

Brown's costs for each band.

Rounded to two decimal places: R589,70.

The difference in the cost of sanitation for the two properties is $\boxed{\text{R}145,74}$.