20. A cyclist can travel 17.6 feet per second. The cyclist would have a better understanding of her speed if it were measured in miles per hour. Which of these completes the expression used to convert the speed of the cyclist to miles per hour?
Answer: C
The expression used to convert the speed of the cyclist to miles per hour is 60 minutes/1 hour = 5280 feet/1 mile.
To convert the cyclist's speed from feet per second to miles per hour, it is essential to understand the relationship between time and distance. The correct conversion expresses that there are 5280 feet in a mile and 60 minutes in an hour, which is necessary for the calculation.
A) 1 hour/60 seconds = 1 mile/5,280 feet
This option incorrectly reverses the relationships needed for the conversion. While it mentions the correct units, it does not correctly express how the time and distance relate to one another for the conversion from feet per second to miles per hour.
B) 60 minutes/1 hour = 1 mile/5280 feet
This option contains the correct units but is arranged incorrectly. It suggests that 1 mile equals 5280 feet, which is true, but it does not facilitate the conversion from feet per second to miles per hour effectively.
C) 60 minutes/1 hour = 5280 feet/1 mile
This option accurately presents the relationship needed for conversion. It states that there are 60 minutes in an hour and 5280 feet in a mile, which is essential for converting the speed from feet per second to miles per hour.
D) 12 inches/1 foot = 60 minutes/1 hour
This option is irrelevant to the conversion of the cyclist's speed. It introduces inches and feet, which are not necessary for converting from feet to miles, and it does not address the relationship needed between time and distance for the conversion.
Conclusion
The correct answer, C, effectively outlines the necessary relationships between time and distance for converting speed from feet per second to miles per hour. Options A and B contain correct units but do not appropriately express the conversion needed, while option D is completely unrelated to the question at hand. Therefore, C is the only option that correctly facilitates the conversion process needed.