the length of bill's backyard swimming pool is 60ft longer than the width of the pool. the surface area of the water is 1600 square feet. what is the width of the pool?

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Bill's new porch is rectangular, with an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?

To find the width of the pool, we first need to set up an equation based on the given information.

Let's assume that the width of the pool is represented by "x" feet.

According to the given information, the length of the pool is 60 feet longer than the width. Therefore, the length of the pool can be represented by "x + 60" feet.

Now, let's calculate the area of the pool, which is given by the formula: length × width.

Area = (x + 60) × x

Since we know that the surface area of the water is 1600 square feet, we can set up the equation:

(x + 60) × x = 1600

Now, let's solve this equation to find the width of the pool:

x(x + 60) = 1600

x^2 + 60x = 1600

Rearranging the equation:

x^2 + 60x - 1600 = 0

Now, we can either factor this quadratic equation or use the quadratic formula to solve for "x". Let's use the quadratic formula.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a, b, and c represent the coefficients of the equation:

a = 1
b = 60
c = -1600

Plugging these values into the quadratic formula:

x = (-(60) ± √((60)^2 - 4(1)(-1600))) / (2(1))

x = (-60 ± √(3600 + 6400)) / 2

x = (-60 ± √(10000)) / 2

x = (-60 ± 100) / 2

Now, we need to calculate both solutions:

Solution 1: (x = (-60 + 100) / 2)
x = 40 / 2
x = 20

Solution 2: (x = (-60 - 100) / 2)
x = -160 / 2
x = -80 (excluded since width cannot be negative)

Therefore, the width of the pool is 20 feet.