4. Peter travels at an average speed of \( 98 \mathrm{~km} / \mathrm{h} \) for 3 hours. He then travels at an average speed of \( 105 \mathrm{~km} / \mathrm{h} \) for 2 hours. 4.1 What was the total distance he travelled? 4.2 Calculate his average speed over the whole distance. A car travels for 2 hours and covers a distance of 240 km . How long will it take to cover a distance of 540 km at the same constant average speed?

Given: - Peter travels at an average speed of \( 98 \, \text{km/h} \) for 3 hours. - Peter then travels at an average speed of \( 105 \, \text{km/h} \) for 2 hours. To find the total distance Peter traveled: 1. Calculate the distance traveled at \( 98 \, \text{km/h} \) for 3 hours: \[ \text{Distance} = \text{Speed} \times \text{Time} = 98 \, \text{km/h} \times 3 \, \text{hours} = 294 \, \text{km} \] 2. Calculate the distance traveled at \( 105 \, \text{km/h} \) for 2 hours: \[ \text{Distance} = \text{Speed} \times \text{Time} = 105 \, \text{km/h} \times 2 \, \text{hours} = 210 \, \text{km} \] 3. Add the distances traveled in both segments to find the total distance: \[ \text{Total Distance} = 294 \, \text{km} + 210 \, \text{km} = 504 \, \text{km} \] Now, to calculate Peter's average speed over the whole distance: \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{504 \, \text{km}}{5 \, \text{hours}} = 100.8 \, \text{km/h} \] Next, to find how long it will take to cover a distance of 540 km at the same constant average speed: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{540 \, \text{km}}{100.8 \, \text{km/h}} \] Let's calculate the time it will take to cover 540 km at the same constant average speed. Calculate the value by following steps: - step0: Calculate: \(\frac{540}{100.8}\) - step1: Convert the expressions: \(\frac{540}{\frac{504}{5}}\) - step2: Multiply by the reciprocal: \(540\times \frac{5}{504}\) - step3: Reduce the numbers: \(15\times \frac{5}{14}\) - step4: Multiply: \(\frac{15\times 5}{14}\) - step5: Multiply: \(\frac{75}{14}\) The time it will take to cover a distance of 540 km at the same constant average speed is approximately 5.357 hours.