Hi, there. I can help with this.

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

We know D = RT, and T is 1/2 hr. In seconds, that's T = 30*60 = 1800 seconds.

Statement #1: The average speed at which Carlos cycled from his house to the library was greater than 16 feet per second.
D = RT > 16*T = 16*1800 = 28800 ft
Since a mile is more than 5000 feet, this distance is under 6 miles. If we know the distance is greater than 28800 ft, we don't know whether it's greater than 6 miles. Statement #1, by itself, is insufficient.

Statement #2: The average speed at which Carlos cycled from his house to the library was less than 18 feet per second.
D = RT < 18T = 18*1800 = 32400 ft
Well, that's a pain in the tuckus --- that's so close we can't estimate: we have to actually multiply out.
6*5280 = 31600 ft ---> that's the exact number of feet in 6 miles.
This statement says the the distance is less than 32400 ft, but we don't know whether it's less than 31600 ft. Therefore, we don't know whether it's less than 6 miles. Statement #2, by itself, is insufficient.

Combined Statement #1 & #2:
Now, we know:

28800 ft < D < 32400 ft

but numbers in that range can be either above or below 31600 ft (six miles), so we can say whether the distance is greater than 6 miles. Even combined, the statements are insufficient.

Answer = E

Does this make sense?

Here' another DS question about average speed:

https://gmat.magoosh.com/questions/926

When you submit an answer to that question, the following page will have a full video explanation.

Let me know if you have any further questions.

Mike