https://file.aiquickdraw.com/mathbot/file/1726617771418nehv8bwk.jpg

In the image, a problem is presented involving a cross-country skier moving between four locations (A, B, C, and D) in a 3-minute time period. Here's how to solve the problem:

### Given Information:
- The skier moves from location **A** to **B** to **C** to **D**.
- The total time of the trip is 3 minutes.
- The distances between the locations are marked on a horizontal scale in meters:
  - **A** is at 0 meters (t=0 min).
  - **B** is at 160 meters (t=1 min).
  - **C** is at 40 meters (t=2 min).
  - **D** is at 120 meters (t=3 min).

### To find:
- **Average Speed** (in meters per minute)
- **Average Velocity** (in meters per minute)

#### 1. **Average Speed**:
   - Average speed is defined as the total distance traveled divided by the total time taken.
   - The skier's path:  
     - From **A** to **B**: 160 meters  
     - From **B** to **C**: 160 - 40 = 120 meters  
     - From **C** to **D**: 120 - 40 = 80 meters  
     - Total distance = 160 + 120 + 80 = 360 meters  
   - Total time = 3 minutes  
   
   So, the average speed = \( \frac{360 \text{ meters}}{3 \text{ minutes}} = 120 \text{ meters per minute} \).

#### 2. **Average Velocity**:
   - Average velocity is defined as the total displacement (straight line from start to finish) divided by the total time.
   - The skier starts at **A** (0 meters) and finishes at **D** (120 meters).
   - Total displacement = 120 meters - 0 meters = 120 meters  
   - Total time = 3 minutes
   
   So, the average velocity = \( \frac{120 \text{ meters}}{3 \text{ minutes}} = 40 \text{ meters per minute} \).

### Final Answers:
- **Average Speed** = 120 meters per minute
- **Average Velocity** = 40 meters per minute

Let me know if you'd like any further details or have questions.

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Here are some related questions:
1. What is the difference between average speed and average velocity in general terms?
2. How would the average speed change if the skier had taken a different path but still ended at location D in 3 minutes?
3. How is displacement different from total distance in physics?
4. If the skier took a longer route to reach the same final position, what would happen to the average velocity?
5. Can the average velocity ever be greater than the average speed?

**Tip:** Remember, velocity is a vector quantity (it has direction), while speed is a scalar (it only has magnitude).

A cross-country skier moves from location A to location B to location C to location D. Each piece of the trip takes 1 minute to complete, and the total time is 3 minutes. The goal is to calculate the average speed (in meters/minute) and the average velocity (in meters/minute) of the skier during the three minutes.

In this problem, a cross-country skier moves between four points (A, B, C, and D), and the task is to calculate the average speed and average velocity over a 3-minute trip. The skier travels 360 meters in total, but their displacement is only 120 meters, leading to different values for average speed (120 m/min) and average velocity (40 m/min).

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