Question

Help! Could I have a step-by-step instruction, please?

Jen is riding her bicycle on a trail at the rate of 0.3 kilometer per minute. Michelle is 11.2 kilometers behind
Jen when she starts traveling on the same trail at a rate of 0.44 kilometer per minute. Let d represent the
distance in kilometers the bicyclists are from the start of the trail and t represent the time in minutes.
The system of equations ⎧
⎨
⎩
d = 0.3t + 11.2
d = 0.44t
can be used to represent this situation. How many minutes
will it take Michelle to catch up to Jen? How far will they be from the start of the trail? Use the substitution
method to solve this real-world application.

Answer 1

Jen rides at 0.3km/minutes and gets a 11.2km head start ahead of Michelle. So her distance equation is d= 0.3t + 11.2

Michelle rides at 0.44km/minute so her distance equation is
d = 0.44t

Both equations give you that persons distance in km in terms of minutes, t.

So Michelle catches up when the distances, d, are equal. Using substitution, you can substitute d = 0.44t into Jen’s equation to get

0.44t = 0.3t + 11.2

Solve for t to get the time to catch up in minutes. Once you have the t value, plug t into either equation and evaluate the distance, d, from the start of the trail.