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

For this case we have the following variables:
 t: number of minutes
 k: number of kilometers
 We have an equation of the form:
 $k = r * t$
 Where,
 r: proportionality constant
 To find r, we must replace a value of k and a value of t.
 We have then:
 $2 = r * 18$
 Clearing r we have:
 $r = 2/18 r = 1/9$
 Substituting we have:
 $k = (1/9) * t$
 We checked for t = 54:
 $k = (1/9) * 54 k = 6$
 Therefore, the equation is correct.
 Answer:
 An equation that can be used to represent k, the number of kilometers Julissa runs in t minutes is:
 $k = (1/9) * t$