In order to swim one mile in a rectangular pool, I must swim the length of the pool 80 times or swim all the way around the perimeter of the pool 22 times. How wide is the pool? (1 mile = 5,280feet)
so would I take 5280 divided by 80 for a total of 66 then subtract 22 from the 66 and that's the width of the pool?
let the length and width be represented by l and w
"80 times the length equals 1 mile" --->
80l=5280
l = 5280/80 = 66
so your first part was right.
perimeter = 2l + 2w
22(2l+2w) = 5280
2l + 2w = 240
l + w = 120, but l=66
66+w = 120
w = 54
To find the width of the pool, you need to determine the distance you swim when you swim the length 80 times and when you swim around the perimeter 22 times.
Let's start with swimming the length of the pool 80 times. You correctly mentioned that you would divide the total distance (1 mile or 5,280 feet) by the number of lengths (80). So, 5,280 divided by 80 equals 66. This tells us that each length is 66 feet.
Now, let's consider swimming around the perimeter of the pool 22 times. To get the distance swum, you need to find the total distance around the pool. This is calculated by adding up the lengths and widths of the rectangular pool.
Since we already know the length is 66 feet, we need to determine the width. To do this, we subtract the number of times you swim the perimeter (22) from the total number of lengths (80), because each time you swim the perimeter, you've already completed one length.
So, 80 - 22 equals 58. This means that when you swim the width of the pool 58 times, it adds up to the same distance as swimming around the perimeter 22 times.
To find the width of the pool, divide the total distance (66 feet per length) by the number of times you swim the width (58). So, 66 divided by 58 equals approximately 1.138 feet.
Therefore, the width of the pool is approximately 1.138 feet.