If it took Carlos 30 minutes to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (Note: 1 mile = 5,280 feet) (1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second. (2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.

Answer:1) No2) YesStep-by-step explanation:Given : If it took Carlos 30 minutes to cycle from his house to the library yesterday.To find : Was the distance that he cycled greater than 6 miles?Solution : The relation between speed , distance and time is [tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second. Speed = 16 feet per secondConverting into miles, [tex]s=\frac{16}{5280}[/tex]Time = 30 minute Converting into seconds, [tex]t=30\times 60[/tex]The distance he covered is [tex]\text{Distance}=\frac{16}{5280}\times30\times 60[/tex][tex]\text{Distance}=5.45\text{ miles}[/tex]No, the distance that he cycled is not greater than 6 miles.2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.Speed = 18 feet per secondConverting into miles, [tex]s=\frac{18}{5280}[/tex]Time = 30 minute Converting into seconds, [tex]t=30\times 60[/tex]The distance he covered is [tex]\text{Distance}=\frac{18}{5280}\times30\times 60[/tex][tex]\text{Distance}=6.13\text{ miles}[/tex]Yes, the distance that he cycled is greater than 6 miles.