To convert 100 inches per minute to feet per minute, we need to use the appropriate conversion factor. The conversion factor between inches and feet is:
[tex]\[ 1 \text{ foot} = 12 \text{ inches} \][/tex]
We will utilize this conversion factor to convert inches to feet.
Given the initial measurement:
[tex]\[ \frac{100 \text{ inches}}{1 \text{ minute}} \][/tex]
We multiply this by the conversion factor that will convert inches to feet:
[tex]\[ \frac{1 \text{ foot}}{12 \text{ inches}} \][/tex]
Now, let's combine these fractions:
[tex]\[ \frac{100 \text{ inches}}{1 \text{ minute}} \times \frac{1 \text{ foot}}{12 \text{ inches}} \][/tex]
When you multiply these fractions, the "inches" units cancel out, and you end up with:
[tex]\[ \frac{100 \times 1 \text{ foot}}{1 \times 12 \text{ minutes}} = \frac{100 \text{ feet}}{12 \text{ minutes}} \][/tex]
This simplifies to:
[tex]\[ \frac{100 \text{ feet}}{12 \text{ minutes}} = 8.333333333333334 \text{ feet per minute} \][/tex]
Therefore, the correct expression that converts 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]
