2.4. Neo can either walk to school at \( 5 \mathrm{~km} / \mathrm{h} \) or ride his bicycle at \( 15 \mathrm{~km} / \mathrm{h} \). If he rides his bicycle, it takes him 10 minutes to get to school. 2.4.1. How long will it take him to walk to school ? 2.4.2. Is this direct or indirect proportion? Give a reason for your answer

1. **Determine the Distance to School** - When Neo rides his bicycle, his speed is \(15 \, \text{km/h}\) and the time taken is \(10\) minutes. First, convert the time into hours: \[ 10 \, \text{minutes} = \frac{10}{60} = \frac{1}{6} \, \text{hours}. \] - Use the formula for distance: \[ \text{Distance} = \text{Speed} \times \text{Time}. \] Substituting the values for the bicycle trip: \[ \text{Distance} = 15 \, \text{km/h} \times \frac{1}{6} \, \text{h} = \frac{15}{6} = 2.5 \, \text{km}. \] 2. **Calculate the Time to Walk to School** - When walking, Neo's speed is \(5 \, \text{km/h}\) and the distance remains \(2.5 \, \text{km}\). Use the formula for time: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}}. \] Substituting the walking values: \[ \text{Time} = \frac{2.5 \, \text{km}}{5 \, \text{km/h}} = 0.5 \, \text{hours}. \] - Convert \(0.5\) hours into minutes: \[ 0.5 \, \text{hours} = 0.5 \times 60 = 30 \, \text{minutes}. \] - **Answer for 2.4.1:** It takes Neo \(30\) minutes to walk to school. 3. **Determine the Proportionality Relationship** - The time taken is calculated using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}}. \] For a constant distance, the time is inversely proportional to the speed. This is because if the speed increases, the time decreases, and vice versa. - **Answer for 2.4.2:** This is an indirect (inverse) proportion since increasing the speed decreases the travel time for a fixed distance.