To find the average speed for the entire round trip, we use the formula:

$\text{Average speed} = \frac{2 \cdot \text{distance}}{\text{time for the entire trip}}$

Step 1: Find the time for each leg of the trip.

• From A to B: The car covers 120 miles at 30 miles per hour. The time taken is:

$\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{120}{30} = 4 \text{ hours}$

• From B to A: The car returns 120 miles at 40 miles per hour. The time taken is:

$\text{Time} = \frac{120}{40} = 3 \text{ hours}$

Step 2: Total time for the round trip.

The total time for the entire trip is:

$\text{Total time} = 4 \text{ hours} + 3 \text{ hours} = 7 \text{ hours}$

Step 3: Total distance for the round trip.

The total distance traveled is:

$\text{Total distance} = 120 \text{ miles} + 120 \text{ miles} = 240 \text{ miles}$

Step 4: Calculate the average speed.

Using the formula for average speed:

$\text{Average speed} = \frac{240 \text{ miles}}{7 \text{ hours}} \approx 34.29 \text{ miles per hour}$

Thus, the average speed for the round trip is approximately 34.29 miles per hour.

Would you like further clarification or details?

Here are 5 related questions:

1. How would the average speed change if the return trip was at 50 miles per hour instead of 40?
2. What if the distance from A to B was doubled but the speeds remained the same?
3. How is average speed different from arithmetic mean speed?
4. What if the car made a stop for 1 hour during the trip? How would that affect the average speed?
5. Can you derive a general formula for average speed given two different speeds over equal distances?

Tip: The average speed for a round trip is not simply the arithmetic mean of the two speeds unless the times are the same. Always use the total distance and total time to compute it properly.