Question

Water flows into a swimming pool at the rate of 8.0 gal/min. The pool is 16 ft wide, 32 ft long and 8.0 ft deep. How long does it take to fill in hours? (1 U.S. gallon = 231 cubic inches)

Answer 1

It takes approximately 37.1451 hours to fill the swimming pool.

Step-by-step explanation:

To calculate the time it takes to fill the swimming pool, we need to determine the volume of the pool first. The volume of the pool can be calculated using the formula:

Volume = length × width × depth

Given that the pool has a width of 16 ft, a length of 32 ft, and a depth of 8 ft, the volume can be calculated as:

Volume = 16 ft × 32 ft × 8 ft = 4096 ft³

Since 1 U.S. gallon is equal to 231 cubic inches, we need to convert the volume from cubic feet to gallons:

Volume = 4096 ft³ × (12 in/ft)³ × (1 gal/231 in³) = 17829.62 gal

Now we can calculate the time it takes to fill the pool by dividing the volume by the rate of water flow:

Time = Volume / Rate = 17829.62 gal / 8.0 gal/min = 2228.7025 min

Converting minutes to hours:

Time = 2228.7025 min × (1 hour/60 min) ≈ 37.1451 hours

Therefore, it takes approximately 37.1451 hours to fill the swimming pool.

Answer 2

1 foot = 12 inches

(1 foot)^3 = (12 inches)^3

1 cubic foot = (12^3) cubic inches

1 cubic foot = 1728 cubic inches, will be used as a conversion factor

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Find the volume of the pool. Assume it is a rectangular prism.

Volume = length*width*height

Volume = 32*16*8

Volume = 4096 cubic feet

Multiply by 1728, which was the conversion factor found earlier, to convert from cubic feet to cubic inches.

4096 cubic feet = (4096*1728) cubic inches = 7077888 cubic inches

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Now use the fact that 1 gallon = 231 cubic inches to convert from cubic inches to gallons

7077888 cubic inches = (7077888 cubic inches)*(1 gallon/231 cubic inches) = 7077888/231 = 30640.2078 gallons which is approximate

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If x is the amount of time in minutes, then 8x gallons of water have been added after x minutes. Set this equal to 30640.2078 and solve for x

8x = 30640.2078

x = 30640.2078/8

x = 3830.02598

Divide this by 60 to convert to hours

3830.02598/60 = 63.8337663

It takes approximately 63.8 hours to fill the pool

This is approximately 63.8/24 = 2.625 days