To address the problem step by step, let's break it down into two main parts: finding the total distance covered and calculating the average speed of the car.
### Finding the Total Distance Covered
1. Determine the distance covered during the first half-hour:
- The car travels at 30 km/h for half an hour.
- Distance covered [tex]\( = \text{speed} \times \text{time} \)[/tex]
- Time (in hours) [tex]\( = 30 \text{ minutes} = 0.5 \text{ hours} \)[/tex]
- Distance [tex]\( = 30 \text{ km/h} \times 0.5 \text{ hours} = 15 \text{ km} \)[/tex]
2. Determine the distance covered during the second half-hour:
- The car travels at 40 km/h for the next half an hour.
- Distance covered [tex]\( = \text{speed} \times \text{time} \)[/tex]
- Time (in hours) [tex]\( = 30 \text{ minutes} = 0.5 \text{ hours} \)[/tex]
- Distance [tex]\( = 40 \text{ km/h} \times 0.5 \text{ hours} = 20 \text{ km} \)[/tex]
3. Calculate the total distance covered:
- Total distance [tex]\( = \text{distance during first half-hour} + \text{distance during second half-hour} \)[/tex]
- Total distance [tex]\( = 15 \text{ km} + 20 \text{ km} = 35 \text{ km} \)[/tex]
### Calculating the Average Speed
1. Calculate the total time traveled:
- The car travels for half an hour at 30 km/h and another half an hour at 40 km/h.
- Total time [tex]\( = 0.5 \text{ hours} + 0.5 \text{ hours} = 1 \text{ hour} \)[/tex]
2. Calculate the average speed:
- Average speed [tex]\( = \frac{\text{total distance}}{\text{total time}} \)[/tex]
- Average speed [tex]\( = \frac{35 \text{ km}}{1 \text{ hour}} = 35 \text{ km/h} \)[/tex]
### Summary
- The total distance covered by the car is 35 km.
- The average speed of the car is 35 km/h.
