Select the correct answer from each drop-down menu.
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 $x$ is her average driving speed in miles/hour.
[tex]\frac{5}{x}+\frac{21}{x+20}[/tex]
The average speed of the train is represented by [ ]. When Megan drives at an average speed of 45 miles/hour, it takes her approximately [ ] to get to work.
Answer (2)
The average speed of the train is represented by x + 20 .
Substitute x = 45 into the expression x 8 + x + 20 21 to find the total commute time.
Calculate the total commute time: 45 8 + 65 21 ≈ 0.50085 hours.
Convert the total commute time to minutes: 0.50085 × 60 ≈ 30.05 minutes. The final answer is $\boxed{30.05}.
Explanation
Understanding the Problem We are given an expression that represents the total time it takes Megan to get to work, which includes an 8-mile drive and a 21-mile train ride. The expression is x 8 + x + 20 21 , where x is her average driving speed in miles/hour. We need to determine the average speed of the train and the total commute time when Megan drives at an average speed of 45 miles/hour.
Finding the Train's Average Speed The average speed of the train is represented by the term x + 20 in the denominator of the second fraction. Since x represents Megan's average driving speed, x + 20 represents the train's average speed, which is 20 miles per hour faster than Megan's driving speed.
Substituting the Driving Speed When Megan drives at an average speed of 45 miles/hour, we substitute x = 45 into the expression to find the total commute time: 45 8 + 45 + 20 21 = 45 8 + 65 21
Calculating Total Commute Time in Hours Now, we calculate the total commute time in hours: 45 8 + 65 21 = 45 × 13 8 × 13 + 65 × 9 21 × 9 = 585 104 + 585 189 = 585 293 ≈ 0.50085 hours
Converting to Minutes and Approximating To convert the total commute time to minutes, we multiply by 60: 0.50085 × 60 ≈ 30.05 minutes Therefore, it takes Megan approximately 30.05 minutes to get to work when she drives at an average speed of 45 miles/hour.
Final Answer The average speed of the train is represented by x + 20 . When Megan drives at an average speed of 45 miles/hour, it takes her approximately 30.05 minutes to get to work.
Examples
Understanding commute times is crucial for urban planning and personal time management. For instance, knowing how changes in driving speed affect overall travel time helps individuals choose the most efficient route or mode of transportation. City planners can use such models to optimize traffic flow and invest in public transport based on commute patterns. By analyzing expressions like the one in this problem, we can make informed decisions about our daily routines and contribute to smarter urban development.
The average speed of the train is represented by x + 20 , which is 65 miles/hour. When Megan drives at an average speed of 45 miles/hour, her total commute time is approximately 30.05 minutes.
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