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Answer:
Approximately [tex]1620\; \text{quart} / \text{hour}[/tex].
Step-by-step explanation:
The given quantity was in the unit [tex]\displaystyle \frac{\text{pint}}{\text{minute}}[/tex] while the required quantity should have the unit [tex]\displaystyle \frac{\text{quart}}{\text{hour}}[/tex]. It would thus be necessary to use conversion factors of the following forms:
[tex]\begin{aligned}\frac{\text{pint}}{\text{minute}} \times \underbrace{\frac{\text{minute}}{\text{hour}} \times \frac{\text{quart}}{\text{pint}}}_{\text{conversion factors}} &= \frac{\text{quart}}{\text{hour}} \end{aligned}[/tex].
Make use of the fact that:
Rearrange the equation [tex]1\; \text{pint} = 0.5\; \text{quart}[/tex] to obtain the conversion factor:
[tex]\begin{aligned} 1 &= \frac{0.5\; \text{quart}}{1\; \text{pint}}\end{aligned}[/tex].
Similarly, rearrange the equation [tex]60\; \text{minute} = 1\; \text{hour}[/tex] to obtain the conversion factor:
[tex]\begin{aligned} 1 &= \frac{1\; \text{hour}}{60\; \text{minute}}\end{aligned}[/tex].
Combine both conversion factors and evaluate:
[tex]\begin{aligned} & 54\; \frac{\text{pint}}{\text{minute}} \\ =\; & 54\; \frac{\text{pint}}{\text{minute}} \times \frac{0.5\; \text{quart}}{1\; \text{pint}} \times \frac{60\; \text{minute}}{1\; \text{hour}} \\ =\; & (54 \times 0.5 \times 60) \; \frac{\text{pint} \times \text{quart} \times \text{minute}}{\text{minute} \times \text{pint} \times \text{hour}} \\=\; & 1620\; \frac{\text{quart}}{\text{hour}}\end{aligned}[/tex].