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?

Answer 1

After running for 18 minutes, Julissa completes 2 kilometers. If she is running a 10-kilometer race at a constant pace, then she comletes 1 kilometer after running 9 minutes. Now you can find the distance she run after 1 minute. This is $\dfrac{1}{9}$ km.

Let t be the time in minutes. Then k, the number of kilometers, can be found from proportion:

$\dfrac{1}{9}\ km$ - 1 minute

k km - t minutes.

Thus,

$\dfrac{\dfrac{1}{9}}{k}=\dfrac{1}{t},\\ \\k=\dfrac{1}{9}\cdot t.$

Answer: $k=\dfrac{1}{9}\cdot t.$

Answer 2

18 mins = 2 km
1 min = 2 ÷ 18 km = 1/9km

at t minutes
 k = t/9 km

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Answer: k = t/9 km
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