1990)
42. A car travels 120 miles from A to B at 30 miles per hour but returns the same distance at 40 miles per hour. What is the average speed for the round trip?

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.

A car travels 120 miles from A to B at 30 miles per hour but returns the same distance at 40 miles per hour. What is the average speed for the round trip?

Learn how to calculate the average speed for a car traveling 120 miles from A to B at 30 mph and returning at 40 mph. This problem demonstrates key concepts of speed, distance, and time calculations with a detailed step-by-step solution. Suitable for students in Grades 7-9.

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