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 variable that depends on another is distance.

Step2: Identify independent variable

The variable that is controlled is time.

Step3: Estimate distance at 40 minutes

Natalie runs 6.8 km in 30 minutes. Assume a linear - like increase. The rate from 0 - 30 minutes is $\frac{6.8}{30}$ km per minute. In 40 minutes, we first find the rate $r=\frac{6.8}{30}$ km/min. Then the distance $d = r\times40=\frac{6.8}{30}\times40=\frac{272}{30}\approx9.07$ 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 9.07 km
4. 6 km/h