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Jon and Austen got in trouble at football practice and have to run laps as a consequence. Jon, who runs at a rate of 3 laps per minute, had completed 10 laps already when he was joined on the track by Austen. Austen's pace is 4 laps per minute. At some point, the two will have run the same distance. How long will that take? Write a system of equations, graph them, and type the solution.

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icetornato
We have two runners, Jon and Austen. Jon runs at a rate of 3 laps per minute, and he has already completed 10 laps when Austen joins him. Austen runs at a rate of 4 laps per minute.

Let's denote the time in minutes it takes for both Jon and Austen to run the same distance as t.

Jon has already completed 10 laps when Austen joins him, so the distance Jon runs is 10 + 3t laps, and the distance Austen runs is 4t laps.

Since they run the same distance, we can set up the equation:

10 + 3t = 4t

Now, we can solve for t:

10 = 4t - 3t
10 = t

So, it will take 10 minutes for Jon and Austen to run the same distance.

Now, we can confirm the solution by observing the graph.

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