To find Cindy's average speed for her morning run, we need to follow these steps:
### Step 1: Understand the distances and times
Cindy runs a total distance of 2 kilometers every morning. Converting this into meters:
[tex]\[ 2 \text{ kilometers} = 2 \times 1000 \text{ meters} = 2000 \text{ meters} \][/tex]
She splits her run into four segments:
1. She takes 2 minutes to run the first 250 meters.
2. She takes 4 minutes to run the next 1,000 meters.
3. She takes 1 minute to run the next 350 meters.
4. She takes 3 minutes to run the remaining distance.
### Step 2: Calculate the remaining distance
First, add up the distances of the first three segments:
[tex]\[ 250 \text{ meters} + 1000 \text{ meters} + 350 \text{ meters} = 1600 \text{ meters} \][/tex]
Now, calculate the remaining distance she needs to run to complete 2 kilometers:
[tex]\[ 2000 \text{ meters} - 1600 \text{ meters} = 400 \text{ meters} \][/tex]
### Step 3: Summarize total distance and time
We have verified that the total distance Cindy runs is 2000 meters.
Next, add up the times for each segment:
1. 2 minutes for the first 250 meters
2. 4 minutes for the next 1,000 meters
3. 1 minute for the next 350 meters
4. 3 minutes for the last 400 meters
Calculate the total time:
[tex]\[ 2 \text{ minutes} + 4 \text{ minutes} + 1 \text{ minute} + 3 \text{ minutes} = 10 \text{ minutes} \][/tex]
### Step 4: Calculate the average speed
The formula for average speed is:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \][/tex]
Using the total distance and total time:
[tex]\[ \text{Average speed} = \frac{2000 \text{ meters}}{10 \text{ minutes}} = 200 \text{ meters per minute} \][/tex]
### Final Answer:
Cindy's average speed for the entire run is [tex]\( 200 \)[/tex] meters per minute.
