Average Speed Concept Explained

The question asks for the average speed of a bus over a journey that consists of two parts with different speeds and distances. Average speed is defined as the total distance traveled divided by the total time taken for the journey.

The formula for average speed ($s_{avg}$) is:

$$s_{avg} = \frac{\text{Total Distance}}{\text{Total Time}}$$

To find the average speed, we first need to calculate the time taken for each part of the journey.

Bus Journey Time Calculation

The journey is divided into two segments:

• Segment 1: Distance ($d_1$) = 80 km, Speed ($s_1$) = 40 km/h
• Segment 2: Distance ($d_2$) = 100 km, Speed ($s_2$) = 50 km/h

We use the relationship: Time = Distance / Speed.

Calculating time for Segment 1 ($t_1$):

$$t_1 = \frac{d_1}{s_1} = \frac{80 \text{ km}}{40 \text{ km/h}} = 2 \text{ hours}$$

Calculating time for Segment 2 ($t_2$):

$$t_2 = \frac{d_2}{s_2} = \frac{100 \text{ km}}{50 \text{ km/h}} = 2 \text{ hours}$$

Total Distance and Time Calculation

Now, we calculate the total distance and total time for the entire journey.

Total Distance ($d_{total}$):

$$d_{total} = d_1 + d_2 = 80 \text{ km} + 100 \text{ km} = 180 \text{ km}$$

Total Time ($t_{total}$):

$$t_{total} = t_1 + t_2 = 2 \text{ hours} + 2 \text{ hours} = 4 \text{ hours}$$

Final Average Speed Calculation

Finally, we calculate the average speed using the total distance and total time.

$$s_{avg} = \frac{d_{total}}{t_{total}} = \frac{180 \text{ km}}{4 \text{ hours}}$$

$$s_{avg} = 45 \text{ km/h}$$

Therefore, the average speed of the bus for the entire journey is 45 km/h.