Final answer:
To cover a mile with sets of 4 size 11 shoeboxes, where each box is 11.197 inches long, one would need 1416 sets because a mile contains 63,360 inches.
Step-by-step explanation:
To solve how many sets of 4 size 11 shoeboxes would be needed to go a mile, we first need to determine the length of one size 11 shoebox. Given that a size 10 shoebox is 11 inches and each subsequent size is half a centimeter bigger, a size 11 would be 11 inches + 0.5 cm. Since there are 2.54 cm in an inch, 0.5 cm is roughly 0.197 inches. Therefore, the size 11 shoebox will be 11.197 inches long. Now to find how many sets of 4 such boxes are needed to cover a mile (63,360 inches), we divide the total inches in a mile by the combined length of 4 shoeboxes (11.197 inches each).
First, calculate the length of 4 shoeboxes: 4 × 11.197 inches = 44.788 inches.
Then, divide the total number of inches in a mile by the length of 4 shoeboxes: 63,360 inches ÷ 44.788 inches ≈ 1415.468 sets. Since we cannot have a fraction of a set, we round up to the nearest whole number, which is 1416 sets.