Jonathan weighs 82kg and is 1.79m tall. Calculate his BMI and determine his weight status. Also, calculate the fuel needed for a round trip from Bloemfontein to Cape Town (1005.6km) if his car uses 8.

The formula for BMI is given as $\text{BMI} = \frac{\text{Weight}}{(\text{Length in m})^2}$.
Given: Weight = 82 kg, Length = 1.79 m.

$$\text{BMI} = \frac{82}{(1.79)^2}$$ $$\text{BMI} = \frac{82}{3.2041}$$ $$\text{BMI} \approx 25.59$$

Based on standard BMI classifications:

• Underweight: < 18.5
• Normal weight: 18.5 – 24.9
• Overweight: 25 – 29.9
• Obese: 30 or greater Jonathan's BMI of 25.59 indicates that he is in the overweight category. Jonathan's weight status is $\boxed{\text{Overweight}}$.

3.2.2
To prepare for the Two Oceans Marathon, Jonathan should aim to reduce his weight to a healthy range through a combination of a balanced diet and a consistent exercise regimen, gradually increasing his fitness level.

3.3.1

Distance from Bloemfontein to Cape Town = 1005.6 km.
For a round trip, the total distance is:

$$\text{Total distance} = 2 \times 1005.6 \text{ km} = 2011.2 \text{ km}$$

Fuel consumption = 8.2 litres per 100 km.

$$\text{Fuel needed} = \frac{2011.2 \text{ km}}{100 \text{ km}} \times 8.2 \text{ litres}$$ $$\text{Fuel needed} = 20.112 \times 8.2 \text{ litres}$$ $$\text{Fuel needed} \approx 164.9184 \text{ litres}$$

Cost of petrol = R19.54 per litre.

$$\text{Total cost} = 164.9184 \text{ litres} \times \text{R}19.54/\text{litre}$$ $$\text{Total cost} \approx \text{R}3222.00$$

Jonathan states that it will cost less than R3 200.00.
Since R3222.00 is not less than R3200.00, Jonathan's statement is $\boxed{\text{incorrect}}$.

3.3.2

Given: Distance = 1005.6 km, Average speed = 95 km/h.
Using the formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$:

$$\text{Driving time} = \frac{1005.6 \text{ km}}{95 \text{ km/h}} \approx 10.58526 \text{ hours}$$

$$10.58526 \text{ hours} = 10 \text{ hours} + (0.58526 \times 60) \text{ minutes}$$ $$10 \text{ hours} + 35.1156 \text{ minutes} \approx 10 \text{ hours and } 35 \text{ minutes}$$

• Colesburg: 1 hour
• Beaufort West: 25 minutes
• Laingsburg: 25 minutes

$$\text{Total stop time} = 1 \text{ hour} + 25 \text{ minutes} + 25 \text{ minutes} = 1 \text{ hour and } 50 \text{ minutes}$$

$$\text{Total travel duration} = \text{Driving time} + \text{Total stop time}$$ $$\text{Total travel duration} = (10 \text{ hours } 35 \text{ minutes}) + (1 \text{ hour } 50 \text{ minutes})$$ $$\text{Total travel duration} = 11 \text{ hours } 85 \text{ minutes}$$

Since 85 minutes is 1 hour and 25 minutes:

$$\text{Total travel duration} = 11 \text{ hours} + 1 \text{ hour } 25 \text{ minutes} = 12 \text{ hours and } 25 \text{ minutes}$$

Departure time = 05:00.

$$\text{Arrival time} = 05:00 + 12 \text{ hours } 25 \text{ minutes} = 17:25$$

Jonathan will arrive in Cape Town at $\boxed{\text{17:25}}$.