Average Speed Calculation Steps

To find the average speed for the entire journey, we need to calculate the total distance traveled and divide it by the total time taken.

1. Calculate Total Distance

The journey consists of four segments:

• A to B: 180 km
• B to C: 240 km
• C to B: 240 km
• B to A: 180 km

Total Distance = Distance(A to B) + Distance(B to C) + Distance(C to B) + Distance(B to A)

\( \text{Total Distance} = 180 \text{ km} + 240 \text{ km} + 240 \text{ km} + 180 \text{ km} = 840 \text{ km} \)

2. Calculate Time for Each Segment

Time is calculated using the formula: Time = Distance / Speed.

• Time (A to B): \( T_{AB} = \frac{180 \text{ km}}{45 \text{ km/h}} = 4 \text{ hours} \)
• Time (B to C): \( T_{BC} = \frac{240 \text{ km}}{60 \text{ km/h}} = 4 \text{ hours} \)
• Time (C to B): \( T_{CB} = \frac{240 \text{ km}}{40 \text{ km/h}} = 6 \text{ hours} \)
• Time (B to A): \( T_{BA} = \frac{180 \text{ km}}{30 \text{ km/h}} = 6 \text{ hours} \)

3. Calculate Total Time Taken

Total Time = Sum of times for all segments.

\( \text{Total Time} = T_{AB} + T_{BC} + T_{CB} + T_{BA} = 4 \text{ h} + 4 \text{ h} + 6 \text{ h} + 6 \text{ h} = 20 \text{ hours} \)

4. Calculate Average Speed

Average speed is defined as Total Distance divided by Total Time.

\( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \)

\( \text{Average Speed} = \frac{840 \text{ km}}{20 \text{ hours}} = 42 \text{ km/h} \)

The average speed for the entire journey is 42 km/h.