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