Question

Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water.

Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.


If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state who paid more to fill her pool. [ 1 ft3 water = 7.48 gallons]

Answer 1

To determine who paid more to fill her pool, we first need to calculate the amount of water each person needs to fill her pool to the required level and then compute the cost based on their respective rates.

Let's start with Theresa's rectangular pool.

1. Calculating the volume of water for Theresa's pool:
The pool is filled to 4 ft - 6 inches = 3.5 ft deep (since 6 inches is 0.5 feet).
Volume of water = Length × Width × Depth
Volume of water = 30 ft × 15 ft × 3.5 ft
Volume of water = 1575 cubic feet

2. Converting cubic feet to gallons:
Since 1 cubic foot of water is equivalent to 7.48 gallons:
Volume of water in gallons = 1575 ft³ × 7.48 gallons/ft³
Volume of water in gallons = 11787 gallons

3. Calculating the cost for Theresa to fill her pool:
The cost to fill the pool is $3.95 per 100 gallons.
Therefore, the total cost = (11787 gallons / 100 gallons) × $3.95
Total cost for Theresa = 117.87 × $3.95
Total cost for Theresa = $465.59

Now let's calculate for Nancy's circular pool.

1. Calculating the volume of water for Nancy's pool:
The diameter of the pool is 24 ft, so the radius r is half of that, r = 24 ft / 2 = 12 ft.
The pool is also filled to 3.5 ft deep.
Volume of water = π × radius² × Depth
Volume of water ≈ 3.14159 × (12 ft)² × 3.5 ft
Volume of water ≈ 3.14159 × 144 ft² × 3.5 ft
Volume of water ≈ 1589.0452 cubic feet

2. Converting cubic feet to gallons:
Volume of water in gallons ≈ 1589.0452 ft³ × 7.48 gallons/ft³
Volume of water in gallons ≈ 11887.658 gallons

3. Calculating the cost for Nancy to fill her pool:
The cost to fill the pool is $200 per 6000 gallons.
Therefore, the total cost = (11887.658 gallons / 6000 gallons) × $200
Total cost for Nancy ≈ 1.981276 × $200
Total cost for Nancy ≈ $396.26

Comparing the costs:

Theresa's cost to fill her pool: $465.59
Nancy's cost to fill her pool: $396.26

Therefore, Theresa paid more to fill her pool.

Answer 2

Explanation:

Both pools were filled 6 inches from the top.

12 inches = 1 feet

6 inches = 6/12 = 0.5 foot

Considering Theresa's pool, it is rectangular. The formula for determining the volume if the rectangular pool is

Volume = length × width × height

Height filled is 4 - 0.5 = 3.5 feet

Volume = 30 × 15 × 3.5 = 1575 ft³

Recall, 1 cubic feet = 7.48 Us gallons

Therefore,

1800 cubic feet = 1575 × 7.48 = 11781 gallons of water

Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water. It means that the amount she paid to fill her pool is

3.95 × 11781/100 = $465.35

Considering Nancy's pool, it is cylindrical. The formula for determining the volume if the cylindrical pool is

Volume = πr²h

Diameter = 24

Radius = diameter/2 = 24/2 = 12 ft

Volume = 3.14 × 12² × 3.5 = 1582.56 ft³. Converting to gallons, it becomes

1582.56 × 7.48 = 11837.55 gallons of water.

Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.

It means that the amount she paid to fill her pool is

200 × 11837.55/6000 = $394.59

Therefore, Theresa paid more to fill her pool.