To solve the problem of finding the average speed of the entire journey, we can follow these steps:
1. Determine the distances traveled in each segment of the trip:
- The first segment of the trip: [tex]\(30 \text{ km}\)[/tex]
- The second segment of the trip: [tex]\(30 \text{ km}\)[/tex]
- The total distance of the trip is [tex]\(120 \text{ km}\)[/tex]. Thus, the remaining distance is:
[tex]\[
120 \text{ km} - 30 \text{ km} - 30 \text{ km} = 60 \text{ km}
\][/tex]
2. Convert the times for each segment into hours:
- The time for the first segment is [tex]\(1 \text{ hour}\)[/tex].
- The time for the second segment is [tex]\(30 \text{ minutes}\)[/tex], which we convert to hours:
[tex]\[
30 \text{ minutes} = \frac{30}{60} = 0.5 \text{ hours}
\][/tex]
- The time for the remaining distance is [tex]\(1 \text{ hour} 30 \text{ minutes}\)[/tex], which we convert to hours:
[tex]\[
1 \text{ hour} 30 \text{ minutes} = 1.5 \text{ hours}
\][/tex]
3. Calculate the total distance traveled:
[tex]\[
30 \text{ km} + 30 \text{ km} + 60 \text{ km} = 120 \text{ km}
\][/tex]
4. Calculate the total time taken:
[tex]\[
1 \text{ hour} + 0.5 \text{ hours} + 1.5 \text{ hours} = 3.0 \text{ hours}
\][/tex]
5. Calculate the average speed of the entire journey:
[tex]\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{120 \text{ km}}{3.0 \text{ hours}} = 40.0 \text{ km/h}
\][/tex]
Therefore, the average speed of the entire journey is [tex]\(40.0 \text{ km/h}\)[/tex].
