Question

practice problem #3
background: natalie sets out to run 15 kilometers. every 10 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 distance depends on time, so it's total distance.

Step2: Identify independent variable

Time is controlled, so it's time.

Step3: Estimate distance at 40 minutes

Find rate between known points and extrapolate.

Step4: Calculate average speed

Use speed formula with total distance and time in hours.

Answer:

1. Total Distance (km)
2. Time (minutes)
3. Assume linear - growth between data points. From 30 minutes (5.8 km) to 60 minutes (10.1 km), rate of change is $\frac{10.1 - 5.8}{60 - 30}=\frac{4.3}{30}$ km/min. In 10 minutes from 30 minutes, distance increase is $\frac{4.3}{30}\times10\approx1.43$ km. So at 40 minutes, distance is $5.8+1.43 = 7.23$ km
4. Total distance $d = 15$ km, total time $t=150$ minutes $=\frac{150}{60}=2.5$ hours. Speed $s=\frac{d}{t}=\frac{15}{2.5}=6$ km/h