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Answer :
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.
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.
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