Let's address each of the questions step by step using the information provided.
1. What is the dependent variable?
In this context, a dependent variable is one that depends on another variable. Here, the total distance run by Natalie changes depending on the time she has been running.
Answer: The dependent variable is "Total Distance (km)".
2. What is the independent variable?
The independent variable is the one that influences or causes changes in the dependent variable. In our context, Natalie checks her running distance at various time intervals. The time she spends running does not depend on the distance; instead, the distance depends on the time.
Answer: The independent variable is "Time (minutes)".
3. How many kilometers had Natalie run after 40 minutes?
Based on the data given:
- At 30 minutes, Natalie had run 6.8 km.
- At 60 minutes, Natalie had run 10.1 km.
To estimate the distance run at 40 minutes, we can apply linear interpolation between these two time points. This means we are assuming a linear increase in distance between the 30-minute and 60-minute marks.
Using the interpolation, the estimated distance Natalie had run at 40 minutes is:
Answer: After 40 minutes, Natalie had run approximately 7.9 km.
4. What was Natalie's average speed (in kilometers per hour) over the course of her run?
To find the average speed, we use the formula:
[tex]\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \][/tex]
Natalie ran a total distance of 15 kilometers. Her total running time was 150 minutes. To convert minutes to hours, we divide by 60:
150 minutes = 150 / 60 = 2.5 hours
Thus, Natalie's average speed is:
[tex]\[ \text{Speed} = \frac{15 \text{ km}}{2.5 \text{ hours}} = 6 \text{ km/hour} \][/tex]
Answer: Natalie's average speed was 6 kilometers per hour.
