Final answer:
Based on the given information, it will take Emily approximately 19.8125 minutes to catch up to Janene.
Step-by-step explanation:
To find out how many minutes it will take Emily to catch up to Janene, we need to determine the distance that Janene runs while Emily catches up. Since Janene starts running 16 minutes before Emily and runs at an average rate of 9 minutes per mile, Janene will have run 16/9 = 1.78 miles before Emily starts running.
Emily runs at an average rate of 8 1/4 minutes per mile. Let's assume it takes Emily two minutes to catch up to Janene. So, when Emily catches up, she would have run a distance equal to t/8 1/4 miles. Since Janene has already run 1.78 miles, the total distance both of them run when Emily catches up is t/8 1/4 + 1.78 miles.
We know that the distance covered by both of them is the same when Emily catches up, so we can equate the distances: t/8 1/4 + 1.78 = t/9
Simplifying the equation, we get: t/8.25 - t/9 = 1.78
Combining the fractions on the left side, we get: (9t - 8.25t)/9*8.25 = 1.78
Solving for t, we get: (0.75t)/9*8.25 = 1.78
Multiplying both sides of the equation by 9*8.25/0.75, we get: t = 1.78 * (9*8.25/0.75)
Using a calculator to evaluate the right side of the equation, we get: t ≈ 19.8125
Therefore, it will take Emily approximately 19.8125 minutes to catch up to Janene.