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Megan's commute to work includes an 8-mile drive and a 21-mile train ride. This expression can be used to find the total time it takes Megan to get to work where [tex]$x$[/tex] is her average driving speed in miles per hour.

[tex]\frac{8}{x} + \frac{21}{x+20}[/tex]

The average speed of the train is represented by [tex]x + 20[/tex]. When Megan drives at an average speed of 45 miles per hour, it takes her approximately [tex]\frac{8}{45} + \frac{21}{65}[/tex] hours to get to work.

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GinnyAnsweridn
Certainly! Let's break down Megan's commute and use the given information to fill in the blanks.

1. Train Speed:
- We know the train speed is 20 miles per hour faster than her driving speed.
- If Megan drives at an average speed of 45 miles per hour, the train speed is [tex]\(45 + 20 = 65\)[/tex] miles per hour.
- So, the average speed of the train is represented by 65 miles per hour.

2. Driving Time:
- The driving distance is 8 miles, and she drives at a speed of 45 miles per hour.
- The time taken to drive is [tex]\(\frac{8}{45}\)[/tex], which is approximately 0.178 hours.

3. Train Time:
- The train distance is 21 miles, and the train speed is 65 miles per hour.
- The time taken for the train ride is [tex]\(\frac{21}{65}\)[/tex], which is approximately 0.323 hours.

4. Total Time:
- The total time for Megan's commute is the sum of the driving time and the train time.
- Total time ≈ 0.178 hours (driving) + 0.323 hours (train) ≈ 0.501 hours.

Therefore, when Megan drives at an average speed of 45 miles/hour, it takes her approximately 0.501 hours to get to work.
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