To convert from inches per minute to feet per minute, we need to use the conversion factor between inches and feet. We know that:
[tex]\[ 1 \text{ foot } = 12 \text{ inches } \][/tex]
This means we need to convert inches to feet by dividing the number of inches by 12.
Given four expressions, let's analyze each one:
1. [tex]\(\frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{60 \text{ minutes}}{1 \text{ hour }}\)[/tex]
- This expression is converting to inches per hour, not feet per minute, so it is not correct for our purpose.
2. [tex]\(\frac{100 \text { inches }}{1 \text { minute }} \times \frac{1 \text { hour }}{60 \text { minutes }}\)[/tex]
- This expression is also solving for time conversion, converting inches per minute to inches per hour, which is also not our target conversion.
3. [tex]\(\frac{100 \text { inches }}{1 \text { minute }} \times \frac{1 \text { foot }}{12 \text { inches }}\)[/tex]
- This expression is correctly converting from inches to feet. The conversion factor [tex]\(\frac{1 \text{ foot }}{12 \text{ inches }}\)[/tex] accurately accounts for the conversion from inches to feet.
- Since 100 inches divided by 12 inches per foot gives us a unit in feet:
[tex]\[
\frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{1 \text{ foot}}{12 \text{ inches}} = \frac{100 \div 12 \text{ feet}}{1 \text{ minute}}
\][/tex]
[tex]\[
\approx 8.333333333333334 \text{ feet per minute}
\][/tex]
4. [tex]\(\frac{100 \text { inches }}{1 \text { minute }} \times \frac{12 \text { inches }}{1 \text { foot }}\)[/tex]
- This expression reverses the conversion factor, converting from inches to inches multiplied by 12, which would result in the unit of measurement being incorrect. Thus, it does not convert to feet.
Therefore, the correct expression to convert 100 inches per minute to feet per minute is:
[tex]\(\frac{100 \text { inches }}{1 \text { minute }} \times \frac{1 \text { foot }}{12 \text { inches }}\)[/tex]
