Final answer:
The width of the walkway around the pool is 2 feet, which is found by setting up an equation based on the given dimensions of the pool and the perimeter of the walkway and solving for the width.
Step-by-step explanation:
The student is trying to calculate the width of a walkway with a uniform width around a rectangular pool with given dimensions and a given perimeter of the walkway. We have a pool that measures 12 feet by 20 feet, and we are told that the perimeter of the walkway around the pool is 80 feet. To find the width of the walkway, we need to add twice the width (2w) to each dimension of the pool, since there will be a walkway on each side.
Let the width of the walkway be w. The new dimensions will be (12+2w) and (20+2w). The perimeter of the rectangle formed by the pool and the walkway is given by 2(12+2w) + 2(20+2w), which must be equal to 80 feet. We obtain the equation:
2(12+2w) + 2(20+2w) = 80
24 + 4w + 40 + 4w = 80
64 + 8w = 80
8w = 80 - 64
8w = 16
w = 2 feet.
Therefore, the width of the walkway is 2 feet.