Suppose you run 4 miles from your house to a​ friend's house at a speed of 4 miles per hour. When the time comes to return​ home, you are tired and walk the same 4 miles home at 3 miles per hour.What is your average speed for the round​ trip?

To find the average speed for the entire round trip, we need to consider the total distance traveled and the total time taken.

### Step 1: Calculate the total distance
The total distance traveled is the sum of the distance to your friend's house and the distance back home:
\[
\text{Total Distance} = 4 \text{ miles} + 4 \text{ miles} = 8 \text{ miles}
\]

### Step 2: Calculate the time taken for each part of the trip
- **Time taken to go to your friend's house**:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{4 \text{ miles}}{4 \text{ miles per hour}} = 1 \text{ hour}
\]
- **Time taken to return home**:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{4 \text{ miles}}{3 \text{ miles per hour}} \approx 1.33 \text{ hours}
\]

### Step 3: Calculate the total time
\[
\text{Total Time} = 1 \text{ hour} + 1.33 \text{ hours} = 2.33 \text{ hours}
\]

### Step 4: Calculate the average speed
The average speed is given by the total distance divided by the total time:
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{8 \text{ miles}}{2.33 \text{ hours}} \approx 3.43 \text{ miles per hour}
\]

So, the average speed for the round trip is approximately **3.43 miles per hour**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the average speed change if you walked both ways?
2. What would be the average speed if you ran both ways?
3. How can you calculate the time taken if you know the average speed and distance?
4. What is the relationship between average speed and harmonic mean?
5. How does changing the speed on one leg of the trip affect the average speed?

**Tip:** When calculating average speed for a round trip with different speeds, remember that it’s not just the average of the two speeds—it depends on the total distance and total time.

Learn how to calculate the average speed for a round trip where you run one way and walk the other. Understand the concepts of speed, distance, and time with a detailed solution example. Suitable for Grades 6-8.

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