Let's break down the solution step by step:
### Step 1: Calculate the speed in feet per minute.
First, we need to find Sam's running speed in feet per minute:
[tex]\[
\text{Speed in feet per minute} = \frac{63,756 \text{ feet}}{70 \text{ minutes}} = 910.8 \text{ feet per minute}
\][/tex]
### Step 2: Convert feet per minute to miles per minute.
Next, we need to convert the speed from feet per minute to miles per minute. We use the fact that 1 mile is 5,280 feet:
[tex]\[
\text{Speed in miles per minute} = \frac{910.8 \text{ feet per minute}}{5,280 \text{ feet per mile}} \approx 0.1725 \text{ miles per minute}
\][/tex]
So the factor used to convert feet per minute into miles per minute is:
[tex]\[
\frac{1 \text{ mile}}{5,280 \text{ feet}}
\][/tex]
### Step 3: Convert miles per minute to miles per hour.
Finally, we need to convert the speed from miles per minute to miles per hour. There are 60 minutes in an hour:
[tex]\[
\text{Speed in miles per hour} = 0.1725 \text{ miles per minute} \times 60 \text{ minutes per hour} = 10.35 \text{ miles per hour}
\][/tex]
So the factor used to convert miles per minute to miles per hour is:
[tex]\[
60 \text{ minutes per hour}
\][/tex]
Therefore, Sam's rate in miles per hour is 10.35 miles per hour.
