To convert 100 inches per minute to feet per minute, we need to use a conversion factor between inches and feet. We know that 1 foot is equal to 12 inches. To convert inches to feet, we divide the number of inches by 12.
Let's break down the options given:
1. [tex]\(\frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{60 \text{ minutes}}{1 \text{ hour}}\)[/tex]
This expression converts inches per minute to inches per hour by multiplying by 60, but we are looking to convert to feet per minute, not per hour.
2. [tex]\(\frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{1 \text{ hour}}{60 \text{ minutes}}\)[/tex]
This expression converts inches per minute to inches per second by multiplying by [tex]\(\frac{1}{60}\)[/tex], which is also not what we need.
3. [tex]\(\frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{1 \text{ foot}}{12 \text{ inches}}\)[/tex]
This is the correct expression. It takes 100 inches per minute and converts it to feet per minute by multiplying by the conversion factor [tex]\(\frac{1 \text{ foot}}{12 \text{ inches}}\)[/tex], which simplifies the inches, leaving us with feet per minute.
4. [tex]\(\frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{12 \text{ inches}}{1 \text{ foot}}\)[/tex]
This expression incorrectly multiplies by 12, which would convert the length into units of inches squared per minute.
Therefore, the correct expression is:
[tex]\[
\frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{1 \text{ foot}}{12 \text{ inches}}
\][/tex]
Evaluating this, we divide 100 by 12:
[tex]\[
\frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{1 \text{ foot}}{12 \text{ inches}} = \frac{100}{12} \text{ feet per minute} = 8.333333333333334 \text{ feet per minute}
\][/tex]
Thus, converting 100 inches per minute gives us approximately 8.333333333333334 feet per minute.
