To calculate the average speed for the entire journey, we need to use the formula for average speed:

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

Step 1: Calculate the total distance

• The person travels 120 km, then 100 km, and finally returns by the same total distance (120 km + 100 km = 220 km). So, the total distance covered in the return trip is also 220 km.

$\text{Total Distance} = 120 + 100 + 220 = 440 \, \text{km}$

Step 2: Calculate the total time

• Time for the first leg (120 km at 80 km/h): $\text{Time}_1 = \frac{120}{80} = 1.5 \, \text{hours}$

• Time for the second leg (100 km at 40 km/h): $\text{Time}_2 = \frac{100}{40} = 2.5 \, \text{hours}$

• Time for the return leg (220 km at 75 km/h): $\text{Time}_3 = \frac{220}{75} \approx 2.93 \, \text{hours}$

Step 3: Calculate the total time

$\text{Total Time} = 1.5 + 2.5 + 2.93 = 6.93 \, \text{hours}$

Step 4: Calculate the average speed

$\text{Average Speed} = \frac{440}{6.93} \approx 63.5 \, \text{km/h}$

Thus, the approximate average speed of the person throughout the journey is 63.5 km/h.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How does the average speed change if the return speed is slower?
2. What happens to the average speed if the distances for each leg are different?
3. How do you calculate the harmonic mean for average speed when only speeds are given?
4. What is the difference between average speed and average velocity in this context?
5. How would the calculation differ if there were additional stops during the journey?

Tip: Always remember that average speed is not simply the arithmetic mean of individual speeds when different distances are involved.