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
use pencil to make graph!

Explanation:

Step1: Identify dependent variable

The total - distance depends on time, so the dependent variable is the total distance Natalie has run.

Step2: Identify independent variable

Time passes regardless of the distance run, so the independent variable is time.

Step3: Estimate distance at 40 minutes

Natalie runs 6.8 km in 30 minutes and 10.1 km in 60 minutes. We can assume a linear - like increase in the short - term. The rate of change from 30 to 60 minutes is $\frac{10.1 - 6.8}{60 - 30}=\frac{3.3}{30}=0.11$ km per minute. From 30 minutes to 40 minutes (10 extra minutes), the additional distance is approximately $0.11\times10 = 1.1$ km. So the distance at 40 minutes is about $6.8+1.1 = 7.9$ km.

Step4: Calculate average speed

The total distance is $d = 15$ km and the total time is $t=150$ 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. Approximately 7.9 km
4. 6 km/h