Question

Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes? How does this work i cant really figure it out

Answer 1

First of all you want to see how long she runs for 1 km and you can figure that out by doing 18/2 and 54/6, they both equal to 9.
So that means that Julissa is running an average of 9 kilometers per minute creating the equation of : t = 9k

Answer 2

For this case, the first thing we must do is define variables.

We have then:

t: the time in minutes

k: the number of kilometers

The relationship between both variables is direct.

Therefore, the function is:

$k (t) = c * t$

Where, "c" is a constant of proportionality.

To determine "c" we use the following data:

After running for 18 minutes, she completes 2 kilometers.

Substituting values:

$2 = c * 18$

Clearing c we have:

$c = \frac{2}{18}$

$c = \frac{1}{9}$

Then, the equation is given by:

$k (t) = \frac{1}{9} * t$

Answer:

An equation that can be used to represent k, the number of kilometers Julissa runs in t minutes is:

$k (t) = \frac{1}{9} * t$