https://file.aiquickdraw.com/mathbot/file/1725769156112g1l21i0v.jpg

Let's analyze the problem shown in the image step-by-step:

### Problem Summary:
- Ethan drove to see his parents.
- He took **4 hours** to cover **4/7** of the journey.
- He covered the remaining **720 km** in **4 hours**.
- We are tasked with finding the **average speed** for the entire journey.

### Steps to Solve:
1. **Determine the total distance of the journey:**
   - Let the total distance be \( D \) km.
   - The first part of the journey is \( \frac{4}{7} \) of the total distance. Therefore, the remaining distance is \( D - \frac{4}{7} D = \frac{3}{7} D \).
   - We know the remaining distance is **720 km**, so we can set up the equation:
     \[
     \frac{3}{7} D = 720
     \]
     Solving for \( D \):
     \[
     D = \frac{720 \times 7}{3} = 1680 \text{ km}
     \]
   So, the total distance of the journey is \( 1680 \) km.

2. **Calculate the total time taken for the journey:**
   - Time for the first part of the journey (covering \( \frac{4}{7} \) of the total distance) is given as **4 hours**.
   - Time for the second part of the journey (720 km) is also **4 hours**.
   - So, the total time taken is:
     \[
     \text{Total time} = 4 + 4 = 8 \text{ hours}
     \]

3. **Calculate the average speed:**
   - Average speed is given by the formula:
     \[
     \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}
     \]
   - The total distance is \( 1680 \) km, and the total time is \( 8 \) hours.
   - Therefore, the average speed is:
     \[
     \text{Average speed} = \frac{1680}{8} = 210 \text{ km/h}
     \]

### Final Answer:
The average speed of Ethan for the whole journey is **210 km/h**.

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Would you like more details on any step? Here are five related questions to expand on this:

1. How do we derive the formula for average speed?
2. What would happen to the average speed if he drove faster during the first part of the journey?
3. Can we calculate the speed for each part of the journey separately?
4. How does proportional distance relate to time in this problem?
5. What if the total time or total distance was unknown—how could we solve this?

**Tip:** When calculating average speed over different segments, remember to add up the total distance and time first before dividing!

Ethan drove to see his parents on weekends. He took 4 hours to cover 4/7 of the journey. He covered the remaining 720 km in 4 hours. What is the average speed of Ethan for the whole journey?

Solve the problem where Ethan drives 4/7 of his journey in 4 hours and covers the remaining 720 km in another 4 hours. Learn how to calculate his total average speed using distance and time relations. Suitable for students in Grades 6-8.

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