This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
3.2.1 Step 1: Calculate Jonathan's Body Mass Index (BMI). The formula for BMI is given as BMI = Weight(Length in m)^2. Given: Weight = 82 kg, Length = 1.79 m. BMI = (82)/((1.79)^2) BMI = (82)/(3.2041) BMI ≈ 25.59 Step 2: Determine Jonathan's weight status. 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 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 Step 1: Calculate the total distance for a round trip. Distance from Bloemfontein to Cape Town = 1005.6 km. For a round trip, the total distance is: Total distance = 2 × 1005.6 km = 2011.2 km Step 2: Calculate the total fuel needed for the round trip. Fuel consumption = 8.2 litres per 100 km. Fuel needed = 2011.2 km100 km × 8.2 litres Fuel needed = 20.112 × 8.2 litres Fuel needed ≈ 164.9184 litres Step 3: Calculate the total cost of petrol for the round trip. Cost of petrol = R19.54 per litre. Total cost = 164.9184 litres × R19.54/litre Total cost ≈ R3222.00 Step 4: Compare the total cost with Jonathan's statement. Jonathan states that it will cost less than R3 200.00. Since R3222.00 is not less than R3200.00, Jonathan's statement is incorrect. 3.3.2 Step 1: Calculate the driving time from Bloemfontein to Cape Town. Given: Distance = 1005.6 km, Average speed = 95 km/h. Using the formula Time = DistanceSpeed: Driving time = 1005.6 km95 km/h ≈ 10.58526 hours Step 2: Convert the driving time to hours and minutes. 10.58526 hours = 10 hours + (0.58526 × 60) minutes 10 hours + 35.1156 minutes ≈ 10 hours and 35 minutes Step 3: Calculate the total time spent on stops. • Colesburg: 1 hour • Beaufort West: 25 minutes • Laingsburg: 25 minutes Total stop time = 1 hour + 25 minutes + 25 minutes = 1 hour and 50 minutes Step 4: Calculate the total travel duration. Total travel duration = Driving time + Total stop time Total travel duration = (10 hours 35 minutes) + (1 hour 50 minutes) Total travel duration = 11 hours 85 minutes Since 85 minutes is 1 hour and 25 minutes: Total travel duration = 11 hours + 1 hour 25 minutes = 12 hours and 25 minutes Step 5: Calculate the arrival time in Cape Town. Departure time = 05:00. Arrival time = 05:00 + 12 hours 25 minutes = 17:25 Jonathan will arrive in Cape Town at 17:25. 3 done, 2 left today. You're making progress.