The traveler claims the map scale is 1:500000. A road distance of 35 km is represented by 14 mm on the map. Is the claim correct? Explain.

Given actual distance = $35 \text{ km}$.
We know that $1 \text{ km} = 1000 \text{ m}$ and $1 \text{ m} = 1000 \text{ mm}$.
So, $1 \text{ km} = 1000 \times 1000 \text{ mm} = 1000000 \text{ mm}$.

$$\text{Actual distance in mm} = 35 \text{ km} \times 1000000 \text{ mm/km} = 35000000 \text{ mm}$$

The map distance is $14 \text{ mm}$.
The scale is given by the ratio of map distance to actual distance.

$$\text{Scale} = \frac{\text{Map distance}}{\text{Actual distance}} = \frac{14 \text{ mm}}{35000000 \text{ mm}}$$

To express this as a ratio $1:X$, we divide both sides by 14:

$$\text{Scale} = 1 : \frac{35000000}{14}$$ $$\text{Scale} = 1 : 2500000$$

The calculated scale is $1 : 2500000$.
The claimed scale is $1 : 500000$.
Since $1 : 2500000 \neq 1 : 500000$, the traveler's claim is incorrect.
The traveler's claim that the map scale is exactly $1 : 500000$ is $\boxed{\text{incorrect}}$.

Question 2.1.3

Given distance = $195 \text{ km}$ and average speed = $105 \text{ km/h}$.

$$\text{Driving time} = \frac{\text{Distance}}{\text{Speed}} = \frac{195 \text{ km}}{105 \text{ km/h}}$$ $$\text{Driving time} = \frac{195}{105} \text{ hours} = \frac{13}{7} \text{ hours}$$

To convert this to hours and minutes:

$$\frac{13}{7} \text{ hours} \approx 1.857 \text{ hours}$$

The whole hour part is 1 hour.
The minutes part is $0.857 \text{ hours} \times 60 \text{ minutes/hour} \approx 51.42 \text{ minutes}$.
So, driving time is approximately 1 hour and 51 minutes (rounding to the nearest minute for practical travel time).

Driving time = 1 hour 51 minutes.
Coffee break = 20 minutes.

$$\text{Total travel time} = 1 \text{ hour } 51 \text{ minutes} + 20 \text{ minutes}$$ $$\text{Total travel time} = 1 \text{ hour } 71 \text{ minutes}$$

Since 71 minutes is 1 hour and 11 minutes:

$$\text{Total travel time} = 1 \text{ hour} + 1 \text{ hour } 11 \text{ minutes} = 2 \text{ hours } 11 \text{ minutes}$$

Departure time = $08:15$.
Add the total travel time (2 hours 11 minutes) to the departure time.

$$08:15 + 2 \text{ hours } 11 \text{ minutes} = 10:26$$

The arrival time in Kokstad is approximately $\boxed{\text{10:26}}$.