To solve this question on average speed, we need to first calculate the total distance traveled and the total time taken.

Given:

1. Speed for the first 2 hours = 40 km/h
2. Speed for the next 4 hours = 50 km/h

Step 1: Calculate the distance covered in each time interval

• Distance = Speed × Time

For the first 2 hours: $\text{Distance}_1 = 40 \, \text{km/h} \times 2 \, \text{hours} = 80 \, \text{km}$

For the next 4 hours: $\text{Distance}_2 = 50 \, \text{km/h} \times 4 \, \text{hours} = 200 \, \text{km}$

Step 2: Calculate the total distance and total time

$\text{Total distance} = \text{Distance}_1 + \text{Distance}_2 = 80 \, \text{km} + 200 \, \text{km} = 280 \, \text{km}$ $\text{Total time} = 2 \, \text{hours} + 4 \, \text{hours} = 6 \, \text{hours}$

Step 3: Calculate the average speed

The formula for average speed is: $\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{280 \, \text{km}}{6 \, \text{hours}} \approx 46.67 \, \text{km/h}$

Thus, the average speed is approximately 46.67 km/h.

Would you like further details on any part of this? Here are 5 related questions you can explore:

1. How does average speed differ from instantaneous speed?
2. How would the average speed change if the bus traveled faster in the first interval?
3. What if the second speed were reduced to 30 km/h for 4 hours? How would that affect the average speed?
4. Can you explain how to calculate the average velocity if direction was involved?
5. How is average speed different from total speed?

Tip: When solving problems involving average speed, always focus on total distance and total time, not the average of individual speeds!