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?

To find the total distance Peter travelled, we can break it down into two parts. For the first part, we multiply his speed by the time: \( 98 \text{ km/h} \times 3 \text{ hours} = 294 \text{ km} \). For the second part, we do the same: \( 105 \text{ km/h} \times 2 \text{ hours} = 210 \text{ km} \). Adding these two distances together gives us \( 294 \text{ km} + 210 \text{ km} = 504 \text{ km} \). Now for calculating the average speed over the whole distance, we need the total time Peter spent travelling, which is \( 3 + 2 = 5 \) hours. The average speed formula is total distance divided by total time. Thus, his average speed is \( 504 \text{ km} / 5 \text{ hours} = 100.8 \text{ km/h} \). Switching gears to the car's journey, based on the information provided, it covers 240 km in 2 hours, translating to a speed of \( 240 \text{ km} / 2 \text{ hours} = 120 \text{ km/h} \). To find out how long it would take to travel 540 km at that same speed, we use the formula time = distance/speed. So, \( 540 \text{ km} / 120 \text{ km/h} = 4.5 \text{ hours} \). Wasn't math just the splendid driver revealing its secrets? Traveling by numbers, oh what a joy!