Question

A swimming pool is being filled at the rate of 54 pt/min (pints per minute). How many quarts per hour is this?

Answer 1

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

.

Answer 2

Answer:

Approximately $1620\; \text{quart} / \text{hour}$.

Step-by-step explanation:

The given quantity was in the unit $\displaystyle \frac{\text{pint}}{\text{minute}}$ while the required quantity should have the unit $\displaystyle \frac{\text{quart}}{\text{hour}}$. It would thus be necessary to use conversion factors of the following forms:

$\begin{aligned}\frac{\text{pint}}{\text{minute}} \times \underbrace{\frac{\text{minute}}{\text{hour}} \times \frac{\text{quart}}{\text{pint}}}_{\text{conversion factors}} &= \frac{\text{quart}}{\text{hour}} \end{aligned}$.

Make use of the fact that:

• $1\; \text{pint} = 0.5\; \text{quart}$, and
• $60\; \text{minute} = 1\; \text{hour}$.

Rearrange the equation $1\; \text{pint} = 0.5\; \text{quart}$ to obtain the conversion factor:

$\begin{aligned} 1 &= \frac{0.5\; \text{quart}}{1\; \text{pint}}\end{aligned}$.

Similarly, rearrange the equation $60\; \text{minute} = 1\; \text{hour}$ to obtain the conversion factor:

$\begin{aligned} 1 &= \frac{1\; \text{hour}}{60\; \text{minute}}\end{aligned}$.

Combine both conversion factors and evaluate:

$\begin{aligned} & 54\; \frac{\text{pint}}{\text{minute}} \\ =\; & 54\; \frac{\text{pint}}{\text{minute}} \times \frac{0.5\; \text{quart}}{1\; \text{pint}} \times \frac{60\; \text{minute}}{1\; \text{hour}} \\ =\; & (54 \times 0.5 \times 60) \; \frac{\text{pint} \times \text{quart} \times \text{minute}}{\text{minute} \times \text{pint} \times \text{hour}} \\=\; & 1620\; \frac{\text{quart}}{\text{hour}}\end{aligned}$.