Water flows through a pipe at a rate of 5700 cups per week. Express this rate of flow in quarts per hour. Round your answer to the nearest hundredth.

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

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

To find the flow rate in quarts per hour from the given rate of 5700 cups per week, we need to convert units step-by-step. Here's how we can do it:

1. Start with the given flow rate:
- 5700 cups per week.

2. Convert cups to quarts:
- First, we need to convert cups to pints. There are 2 cups in a pint:
[tex]\[
\frac{5700 \text{ cups}}{2} = 2850 \text{ pints}
\][/tex]

- Then, convert pints to quarts. There are 2 pints in a quart:
[tex]\[
\frac{2850 \text{ pints}}{2} = 1425 \text{ quarts}
\][/tex]

So, the flow rate is 1425 quarts per week.

3. Convert weeks to hours:
- There are 7 days in a week and 24 hours in a day:
[tex]\[
7 \text{ days/week} \times 24 \text{ hours/day} = 168 \text{ hours/week}
\][/tex]

4. Calculate the flow rate in quarts per hour:
- Divide the number of quarts per week by the number of hours per week:
[tex]\[
\frac{1425 \text{ quarts}}{168 \text{ hours}} \approx 8.482142857142858 \text{ quarts/hour}
\][/tex]

5. Round the result:
- Finally, round the result to the nearest hundredth:
[tex]\[
8.48 \text{ quarts/hour}
\][/tex]

Thus, the flow rate is approximately 8.48 quarts per hour.