Understanding the Problem: Pudge’s Bicycle Ride
On his way home, Pudge first rode his bike around the perimeter of the park, which took 5 2/5 minutes, then it took 8 1/10 minutes to ride home. How long did it take Pudge to get home? This problem involves understanding and manipulating mixed numbers, as well as applying basic arithmetic to determine total time. To find the total duration of Pudge’s journey, we need to analyze each segment separately and then combine the times. In this article, we will explore the steps involved in solving this problem, converting mixed numbers to improper fractions, performing addition, and interpreting the results.
Breaking Down the Problem
Identifying Each Segment of the Journey
- First Segment: Riding around the park’s perimeter
- Second Segment: Riding from the park to his home
Given Times
- Time around the park: 5 2/5 minutes
- Time to ride home: 8 1/10 minutes
What Is Being Asked?
The main question is: How long did it take Pudge to get home? Since the first segment involves riding around the park, which is a different route, and the second segment is from the park to home, the total time Pudge spent on his journey includes both segments. However, the problem emphasizes the time to ride home, which is the second segment, and the total journey time if combined.
Converting Mixed Numbers to Improper Fractions
Why Convert to Improper Fractions?
Mixed numbers are convenient for reading but complicate calculations. Converting them to improper fractions simplifies addition, subtraction, and other operations involving fractions.
Converting 5 2/5 to an Improper Fraction
- Multiply the whole number by the denominator: 5 × 5 = 25
- Add the numerator: 25 + 2 = 27
- Write as a fraction: 27/5
Converting 8 1/10 to an Improper Fraction
- Multiply the whole number by the denominator: 8 × 10 = 80
- Add the numerator: 80 + 1 = 81
- Write as a fraction: 81/10
Adding the Times: Total Journey Duration
Finding a Common Denominator
To add 27/5 and 81/10, we need a common denominator. The least common denominator (LCD) of 5 and 10 is 10.
Rewriting Fractions with Common Denominator
- 27/5: multiply numerator and denominator by 2 to get 54/10
- 81/10 remains the same
Performing the Addition
Now, add the two fractions:
- 54/10 + 81/10 = (54 + 81)/10 = 135/10
Simplifying the Result
Divide numerator and denominator by their greatest common divisor, which is 5:
- 135 ÷ 5 = 27
- 10 ÷ 5 = 2
So, 135/10 simplifies to 27/2.
Converting the Total Time Back to a Mixed Number
Dividing the Improper Fraction
To interpret the total time, divide 27 by 2:
- 27 ÷ 2 = 13 with a remainder of 1
- Expressed as a mixed number: 13 1/2
Final Answer
Therefore, Pudge’s total journey time, combining both segments, is 13 1/2 minutes.
Interpreting the Results in Context
What Does 13 1/2 Minutes Mean?
The total time of 13 1/2 minutes (or 13 minutes and 30 seconds) indicates that Pudge spent this amount of time traveling from the point he left the park to his home, including his ride around the park perimeter and the final leg home.
Additional Considerations
- Understanding the significance of each segment’s duration helps in planning or estimating travel times.
- If Pudge’s route or speed varies, the actual times might differ, but based on the given data, this is the total time assuming consistent speed.
Summary of the Calculation Steps
- Convert mixed numbers to improper fractions.
- Find a common denominator to add fractions.
- Add the fractions and simplify the result.
- Convert the sum back into a mixed number for easy interpretation.
- Interpret the total time in minutes and seconds.
Conclusion: How Long Did Pudge Take to Get Home?
By following the process of converting mixed numbers, adding fractions, and simplifying, we determined that Pudge’s total journey time was 13 1/2 minutes. This comprehensive approach demonstrates the importance of understanding fractions in real-world problems and highlights the steps needed to perform accurate calculations. Whether for a school assignment or just everyday problem-solving, mastering these skills is essential for effective mathematical reasoning.
