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

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

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}} * \underbrace{\frac{\text{minute}}{\text{hour}} * \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}} * \frac{0.5\; \text{quart}}{1\; \text{pint}} * \frac{60\; \text{minute}}{1\; \text{hour}} \\ =\; & (54 * 0.5 * 60) \; \frac{\text{pint} * \text{quart} * \text{minute}}{\text{minute} * \text{pint} * \text{hour}} \\=\; & 1620\; \frac{\text{quart}}{\text{hour}}\end{aligned}`.