Question

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

1) No

2) Yes

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

`\text{Distance}=\text{Speed}* \text{Time}`

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 second

Converting into miles,
`s=(16)/(5280)`

Time = 30 minute

Converting into seconds,
`t=30* 60`

The distance he covered is

`\text{Distance}=(16)/(5280)*30* 60`

`\text{Distance}=5.45\text{ miles}`

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 second

Converting into miles,
`s=(18)/(5280)`

Time = 30 minute

Converting into seconds,
`t=30* 60`

The distance he covered is

`\text{Distance}=(18)/(5280)*30* 60`

`\text{Distance}=6.13\text{ miles}`

Yes, the distance that he cycled is greater than 6 miles.