Water flows into a swimming pool at a rate of 9.59 gal/min. If the pool dimensions are 30.9 ft wide, 47.6 ft long and 13 ft deep, how long does it take to fill the pool? (1 gallon = 231 cubic inches). Answer in units of minutes.
Divide the pool volume (in gallons) by 9.59 gal/min
V = 19,121 ft^3 * 1 gallon/231in^3 * 1728in^3/ft^3 = 143,035 gal.
First, we need to calculate the volume of the swimming pool. The formula for the volume of a rectangular prism is:
Volume = length × width × depth
Given:
Width = 30.9 ft
Length = 47.6 ft
Depth = 13 ft
Volume = 30.9 ft × 47.6 ft × 13 ft
Now we need to convert the volume from cubic feet to gallons. We know that 1 gallon is equal to 231 cubic inches, and there are 12 inches in 1 foot. So, to convert cubic feet to gallons, we'll use the following conversion factors:
1 cubic foot = 12 inches × 12 inches × 12 inches = 1728 cubic inches
1 gallon = 231 cubic inches
Volume = (30.9 ft × 12 inches/ft) × (47.6 ft × 12 inches/ft) × (13 ft × 12 inches/ft) / 231 cubic inches/gallon
Now let's calculate the volume in gallons:
Volume = (30.9 × 12) × (47.6 × 12) × (13 × 12) / 231 gallons
Volume = 45241.92 gallons
Next, we need to determine how long it will take to fill the pool at a rate of 9.59 gallons per minute:
Time = Volume / Rate
Time = 45241.92 gallons / 9.59 gal/min
Time ≈ 4714.005 minutes
Therefore, it will take approximately 4714.005 minutes to fill the pool.
To find out how long it takes to fill the pool, we need to determine the volume of the pool and then divide it by the rate at which water flows into the pool.
First, let's convert the pool dimensions from feet to inches, since the conversion rate for gallons provided is in cubic inches.
The width of the pool is 30.9 ft, so it is 30.9 * 12 = 370.8 inches wide.
The length of the pool is 47.6 ft, so it is 47.6 * 12 = 571.2 inches long.
The depth of the pool is 13 ft, so it is 13 * 12 = 156 inches deep.
Now, let's calculate the volume of the pool in cubic inches. Since the pool has a rectangular shape, we can use the formula: volume = length * width * depth.
The volume of the pool is 571.2 * 370.8 * 156 = 32,105,497.6 cubic inches.
Next, let's convert the volume from cubic inches to gallons using the provided conversion rate of 1 gallon = 231 cubic inches.
The volume of the pool in gallons is 32,105,497.6 / 231 = 138,993.9 gallons.
Now, we can calculate the time it takes to fill the pool by dividing the volume of the pool by the rate of water flow.
Time = Volume / Rate
Time = 138,993.9 gallons / 9.59 gal/min
Dividing the volume by the rate gives us the time in minutes.
Time = 14,476.3 minutes
Therefore, it takes approximately 14,476.3 minutes to fill the pool.