Question

sam ran 63,756 feet in 70 minutes. what is sams rate in miles per hour? (there are 5,280 feet in one mile.)
step 1: what is sams rate as stated?
63,756 feet
70 minutes
$=\frac{63,756\text{ ft}}{70\text{ min}}$
step 2: what factor is used to convert feet per minute into miles per minute?

Explanation:

Step1: Identify given rate

$\text{Given rate} = \frac{63,756\ \text{ft}}{70\ \text{min}}$

Step2: Find feet-to-mile conversion

We know $1\ \text{mile}=5,280\ \text{feet}$, so the conversion factor to turn feet to miles is $\frac{1\ \text{mile}}{5,280\ \text{feet}}$

Step3: (Full rate calculation, extra context)

First convert feet to miles:
$\frac{63,756\ \text{ft}}{70\ \text{min}} \times \frac{1\ \text{mile}}{5,280\ \text{feet}} = \frac{63,756}{70 \times 5,280}\ \text{miles/min}$
Then convert minutes to hours (multiply by 60):
$\frac{63,756 \times 60}{70 \times 5,280}\ \text{miles/hour} = 10.35\ \text{miles/hour}$

Answer:

1. $\frac{63,756\ \text{ft}}{70\ \text{min}}$
2. $\frac{1\ \text{mile}}{5,280\ \text{feet}}$