Final answer:
One lap around a rectangular track that is 2000 feet by 640 feet equals one mile. This is because the perimeter of the track is 5280 feet, which is also the distance in one mile. When converting 6 miles to feet, we multiply 6 by 5280, resulting in 31,680 feet.
Step-by-step explanation:
The student is asking about the conversion of miles to feet and determining how many laps around a track would equate to a mile. The track is given to be 2000 feet by 640 feet. Since the perimeter of a rectangle is the sum of all four sides, we first calculate the perimeter of the track:
Perimeter = 2(length + width) = 2(2000 feet + 640 feet) = 2(2640 feet) = 5280 feet
Now, since one mile is 5280 feet, we can see that one lap around this rectangular track is exactly one mile. Therefore, to run one mile, the student only needs to run around the track one time.
For the additional part of the question involving a conversion from miles to feet:
If the actual distance is 6 miles, we can use the fact that 1 mile equals 5280 feet. We set up a proportion:
1 mile/5280 feet = 6 miles/x feet
Cross multiply to solve for x:
1 * x = 6 * 5280
x = 31,680
So, 6 miles is equivalent to 31,680 feet.