To solve the problem, we need to determine the total distance traveled by the car and the average speed of the car. The car travels at two different speeds for two different time intervals.
Let's break down the steps:
### Given Data:
1. Speed during the first part of the journey: 30 km/hr
2. Speed during the second part of the journey: 40 km/hr
3. Time during the first part of the journey: 5 minutes
4. Time during the second part of the journey: 10 minutes
We need to convert time from minutes to hours since the speeds are given in km/hr.
### Conversion of Time:
- Time during the first part: [tex]\( \frac{5 \text{ minutes}}{60} = \frac{5}{60} \)[/tex] hours = 0.0833 hours
- Time during the second part: [tex]\( \frac{10 \text{ minutes}}{60} = \frac{10}{60} \)[/tex] hours = 0.1667 hours
### Calculation of Distances:
The formula to calculate distance is:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]
1. Distance traveled during the first part:
[tex]\[ \text{Distance}_1 = 30 \text{ km/hr} \times 0.0833 \text{ hours} = 2.5 \text{ km} \][/tex]
2. Distance traveled during the second part:
[tex]\[ \text{Distance}_2 = 40 \text{ km/hr} \times 0.1667 \text{ hours} = 6.667 \text{ km} \][/tex]
### Total Distance Traveled:
[tex]\[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 2.5 \text{ km} + 6.667 \text{ km} = 9.167 \text{ km} \][/tex]
### Total Time Traveled:
[tex]\[ \text{Total Time} = 0.0833 \text{ hours} + 0.1667 \text{ hours} = 0.25 \text{ hours} \][/tex]
### Average Speed:
The formula to calculate average speed is:
[tex]\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \][/tex]
[tex]\[ \text{Average Speed} = \frac{9.167 \text{ km}}{0.25 \text{ hours}} = 36.667 \text{ km/hr} \][/tex]
### Summary:
(i) The total distance traveled by the car is [tex]\( 9.167 \)[/tex] km.
(ii) The average speed of the car is [tex]\( 36.667 \)[/tex] km/hr.
