Calculate the actual distance between Keetmanshoop and Windhoek, and determine the number scale of the map.

The route from Keetmanshoop to Windhoek passes through Mariental and Rehoboth.

$$\text{Distance (Keetmanshoop to Mariental)} = 221 \text{ km}$$ $$\text{Distance (Mariental to Rehoboth)} = 83 \text{ km}$$ $$\text{Distance (Rehoboth to Windhoek)} = 87 \text{ km}$$ $$\text{Total actual distance} = 221 \text{ km} + 83 \text{ km} + 87 \text{ km} = 391 \text{ km}$$

To calculate the number scale, you would need to physically measure the distance between Keetmanshoop and Windhoek on the map using a ruler. Let's say this measured distance is $X$ cm.
The scale would then be calculated as:

$$\text{Scale} = \frac{\text{Measured distance on map (in cm)}}{\text{Actual distance (in cm)}}$$

Since $1 \text{ km} = 100,000 \text{ cm}$, the actual distance in cm is $391 \times 100,000 \text{ cm} = 39,100,000 \text{ cm}$.
If, for example, the measured distance on the map was $10 \text{ cm}$, the scale would be $\frac{10 \text{ cm}}{39,100,000 \text{ cm}} = \frac{1}{3,910,000}$.
As an AI, I cannot perform the physical measurement on the image, so I cannot provide a numerical value for the map scale.

The actual distance from Keetmanshoop to Windhoek is:

$$\boxed{\text{391 km}}$$

The route from Gobabis to Grootfontein passes through Otjiwarongo.

$$\text{Distance (Gobabis to Otjiwarongo)} = 233 \text{ km}$$ $$\text{Distance (Otjiwarongo to Grootfontein)} = 157 \text{ km}$$ $$\text{Total actual distance} = 233 \text{ km} + 157 \text{ km} = 390 \text{ km}$$

The actual distance from Gobabis to Grootfontein is:

$$\boxed{\text{390 km}}$$

$$\text{Distance} = 390 \text{ km}$$ $$\text{Speed} = 90 \text{ km/hour}$$ $$\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{390 \text{ km}}{90 \text{ km/hour}} = \frac{39}{9} \text{ hours} = \frac{13}{3} \text{ hours}$$

$$\text{Time} = 4 \frac{1}{3} \text{ hours}$$

To convert $\frac{1}{3}$ of an hour to minutes:

$$\frac{1}{3} \times 60 \text{ minutes} = 20 \text{ minutes}$$

So, the travel time is 4 hours and 20 minutes.

Departure time: 7:45
Travel time: 4 hours 20 minutes

$$\text{Arrival time} = 7:45 + 4 \text{ hours } 20 \text{ minutes} = 11:65$$

Since 65 minutes is 1 hour and 5 minutes, the arrival time is 12:05.

Calculated arrival time: 12:05
Stated arrival time: 12:00
Amukele's timing is incorrect because he would arrive 5 minutes later than he stated.

$$\boxed{\text{Incorrect}}$$

$$\text{Distance} = 390 \text{ km}$$ $$\text{Petrol consumption} = 8 \text{ litres per } 100 \text{ km}$$ $$\text{Litres needed} = \frac{390 \text{ km}}{100 \text{ km}} \times 8 \text{ litres} = 3.9 \times 8 \text{ litres} = 31.2 \text{ litres}$$

$$\text{Cost per litre} = \text{R}16.45$$ $$\text{Total cost} = 31.2 \text{ litres} \times \text{R}16.45/\text{litre} = \text{R}513.24$$

The cost of petrol to travel from Gobabis to Grootfontein is:

$$\boxed{\text{R513.24}}$$