Question

practice problem #3
background: natalie sets out to run 15 kilometers. every 30 minutes she checked her pedometer to determine how far she had run. use the data below to create a proper scientific graph and to answer the corresponding questions.

time (minutes)	total distance (km)
30	6.8
60	10.1
90	12
120	13.3
150	15

1. what is the dependent variable?
2. what is the independent variable?
3. how many kilometers had natalie run after 40 minutes?
4. what was natalie’s average speed (in kilometers per hour) over the course of her run? use the formula speed = distance / time

Explanation:

Step1: Identify dependent variable

The total distance depends on time, so it's the dependent variable.

Step2: Identify independent variable

Time progresses on its own and affects the distance, so time is the independent variable.

Step3: Estimate distance at 40 minutes

Assume linear - like behavior between 30 and 60 minutes. In 30 minutes (from 30 to 60), the distance changes by \(10.1 - 6.8=3.3\) km. The rate in this interval is \(\frac{3.3}{30}=0.11\) km per minute. From 30 minutes to 40 minutes (10 minutes), the additional distance is \(0.11\times10 = 1.1\) km. So the distance at 40 minutes is \(6.8+1.1 = 7.9\) km.

Step4: Calculate average speed

The total distance \(d = 15\) km and the total time \(t=150\) minutes. Convert time to hours: \(t=\frac{150}{60}=2.5\) hours. Using the formula \(v=\frac{d}{t}\), we have \(v=\frac{15}{2.5}=6\) km/h.

Answer:

1. Total Distance (km)
2. Time (minutes)
3. 7.9 km
4. 6 km/h