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Water flows through a pipe at a rate of 5 quarts per month. Express this rate of flow in fluid ounces per hour. Round your answer to the nearest hundredth.

*Note: you must use these exact conversion factors to get this question right.

\begin{tabular}{|c|c|}
\hline
Volume & Time \\
\hline
1 cup [tex]$(\operatorname{cup}) = 8$[/tex] fluid ounces [tex]$(\operatorname{floz})$[/tex] & 1 minute [tex]$(\min) = 60$[/tex] seconds [tex]$(\sec)$[/tex] \\
\hline
1 pint [tex]$(\operatorname{pt}) = 2$[/tex] cups [tex]$(\operatorname{cups})$[/tex] & 1 hour [tex]$(\operatorname{hr}) = 60$[/tex] minutes [tex]$(\min)$[/tex] \\
\hline
1 quart [tex]$(\operatorname{qt}) = 2$[/tex] pints [tex]$(\operatorname{pt})$[/tex] & 1 day [tex]$(\operatorname{day}) = 24$[/tex] hours [tex]$(\operatorname{hr})$[/tex] \\
\hline
1 gallon [tex]$(\operatorname{gal}) = 4$[/tex] quarts [tex]$(\operatorname{qt})$[/tex] & 1 week [tex]$(\operatorname{week}) = 7$[/tex] days [tex]$(\operatorname{days})$[/tex] \\
\hline
1 cubic foot [tex]$\left(\operatorname{ft}^3\right) = 7.481$[/tex] gallons [tex]$(\operatorname{gal})$[/tex] & 1 month [tex]$(\operatorname{month}) = 30$[/tex] days [tex]$(\operatorname{days})$[/tex] \\
\hline
1 liter [tex]$(\operatorname{L}) = 1000$[/tex] milliliters [tex]$(\operatorname{mL})$[/tex] & 1 year [tex]$(\operatorname{year}) = 365$[/tex] days [tex]$(\operatorname{days})$[/tex] \\
\hline
1 cubic meter [tex]$\left(\operatorname{m}^3\right) = 1000$[/tex] liters [tex]$(\operatorname{L})$[/tex] & \\
\hline
1 gallon [tex]$(\operatorname{gal}) = 3.785$[/tex] liters [tex]$(\operatorname{L})$[/tex] & \\
\hline
1 fluid ounce [tex]$\left(\operatorname{floz}\right) = 29.574$[/tex] milliliters [tex]$(\operatorname{mL})$[/tex] & \\
\hline
\end{tabular}

Answer :

Sure, let's solve this step-by-step to express the flow rate in fluid ounces per hour.

1. Start with the given flow rate:
- Water flows through a pipe at a rate of 5 quarts per month.

2. Conversion factors provided:
- 1 quart = 2 pints
- 1 pint = 2 cups
- 1 cup = 8 fluid ounces
- 1 month = 30 days
- 1 day = 24 hours

3. Convert quarts to fluid ounces:
- First, convert quarts to pints:
[tex]\[
5 \text{ quarts} \times 2 \text{ pints/quart} = 10 \text{ pints}
\][/tex]
- Next, convert pints to cups:
[tex]\[
10 \text{ pints} \times 2 \text{ cups/pint} = 20 \text{ cups}
\][/tex]
- Finally, convert cups to fluid ounces:
[tex]\[
20 \text{ cups} \times 8 \text{ fluid ounces/cup} = 160 \text{ fluid ounces}
\][/tex]

4. Convert the time from months to hours:

- First, convert months to days:
[tex]\[
1 \text{ month} = 30 \text{ days}
\][/tex]
- Then, convert days to hours:
[tex]\[
30 \text{ days} \times 24 \text{ hours/day} = 720 \text{ hours}
\][/tex]

5. Calculate the rate in fluid ounces per hour:
- We now have 160 fluid ounces per month and 720 hours per month.
[tex]\[
\text{Rate in fluid ounces per hour} = \frac{160 \text{ fluid ounces}}{720 \text{ hours}} = 0.2222\ldots \text{ fluid ounces/hour}
\][/tex]

6. Round the answer to the nearest hundredth:
[tex]\[
0.22 \text{ fluid ounces/hour}
\][/tex]

Therefore, the flow rate is approximately [tex]\(0.22\)[/tex] fluid ounces per hour.

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