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At the Olympic Games, a runner won the 26.2-mile marathon race in 2 hr 2 min and 3 second. What was his average speed in mph and km/h? ...

At the Olympic Games, a runner won the 26.2-mile marathon race in 2 hr 2 min and 3 second. What was his average speed in mph and km/h? ...

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Calculating Average Speed in mph and km/h #### Problem Statement: At the Olympic Games, a runner won the 26.2-mile marathon race in 2 hr 2 min and 3 seconds. What was his average speed in mph and km/h? --- #### Solution: First, convert the time into hours: - Minutes and seconds need to be converted to a fraction of an hour. - \( \text{Total Time} = 2 \text{ hours} + \frac{2 \text{ minutes}}{60} + \frac{3 \text{ seconds}}{3600} \) - Calculation: \( 2 + \frac{2}{60} + \frac{3}{3600} \approx 2.0342 \text{ hours} \) Next, find the average speed in mph: - Speed (mph) = Distance (miles) / Time (hours) - \( \text{Speed (mph)} = \frac{26.2 \text{ miles}}{2.0342 \text{ hours}} \approx 12.9 \text{ mph} \) To convert the speed to km/h: - Use the conversion factor, \(1 \text{ mile} = 1.60934 \text{ kilometers}\) - \( 12.9 \text{ mph} \times 1.60934 \approx 20.8 \text{ km/h} \) #### Conclusion: The average speed of the runner is approximately: - \(12.9\) mph - \(20.8\) km/h (Responses should be typed as an integer or a decimal rounded to the nearest tenths as needed.)
Transcribed Image Text:### Calculating Average Speed in mph and km/h #### Problem Statement: At the Olympic Games, a runner won the 26.2-mile marathon race in 2 hr 2 min and 3 seconds. What was his average speed in mph and km/h? --- #### Solution: First, convert the time into hours: - Minutes and seconds need to be converted to a fraction of an hour. - \( \text{Total Time} = 2 \text{ hours} + \frac{2 \text{ minutes}}{60} + \frac{3 \text{ seconds}}{3600} \) - Calculation: \( 2 + \frac{2}{60} + \frac{3}{3600} \approx 2.0342 \text{ hours} \) Next, find the average speed in mph: - Speed (mph) = Distance (miles) / Time (hours) - \( \text{Speed (mph)} = \frac{26.2 \text{ miles}}{2.0342 \text{ hours}} \approx 12.9 \text{ mph} \) To convert the speed to km/h: - Use the conversion factor, \(1 \text{ mile} = 1.60934 \text{ kilometers}\) - \( 12.9 \text{ mph} \times 1.60934 \approx 20.8 \text{ km/h} \) #### Conclusion: The average speed of the runner is approximately: - \(12.9\) mph - \(20.8\) km/h (Responses should be typed as an integer or a decimal rounded to the nearest tenths as needed.)
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