Mathematics, 26.06.2020 16:01 Moocow17

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)

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Answer from: amandanunnery33

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

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

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

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

Answer from: Quest

10010010001010010101001001010010100101010010101010010010101010110010001011010010010001

step-by-step explanation:

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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