To solve this problem, we need to calculate the average speed of David over the entire distance.

The formula for average speed is:

$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$

Step 1: Determine the total distance

David's total distance is: $300 \, \text{km} + 400 \, \text{km} + 200 \, \text{km} + 300 \, \text{km} = 1200 \, \text{km}.$

Step 2: Calculate the time taken for each segment of the journey

For each segment, the time taken is: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

1. By aeroplane: $\text{Time} = \frac{300}{150} = 2 \, \text{hours}.$

2. By train: $\text{Time} = \frac{400}{40} = 10 \, \text{hours}.$

3. By car: $\text{Time} = \frac{200}{50} = 4 \, \text{hours}.$

4. By bike: $\text{Time} = \frac{300}{60} = 5 \, \text{hours}.$

Step 3: Calculate the total time

$\text{Total Time} = 2 + 10 + 4 + 5 = 21 \, \text{hours}.$

Step 4: Calculate the average speed

Using the formula for average speed: $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{1200}{21}.$

Performing the division: $\frac{1200}{21} = 57 \frac{1}{7} \, \text{km/h}.$

Final Answer:

The average speed of the entire journey is: $\boxed{57 \frac{1}{7} \, \text{km/h}}$

If you want additional clarifications or details, feel free to ask!

5 Related Questions:

1. How do we handle average speed for uneven time intervals?
2. What is the difference between average speed and instantaneous speed?
3. Can we calculate total time directly using weighted averages of speeds?
4. What happens to average speed if one segment is extremely slow?
5. Why is average speed not the arithmetic mean of individual speeds?

1 Tip:

Always ensure you compute total distance and total time separately to avoid confusion in average speed problems.