To convert a speed from inches per minute to feet per minute, you need to use the relationship between inches and feet. Specifically, there are 12 inches in 1 foot.
So, to make this conversion, you use a factor that allows you to cancel out the inches unit and bring in the feet unit.
Given that:
[tex]\[ \frac{100 \text { inches }}{1 \text { minute }} \][/tex]
You need to multiply this by the conversion factor from inches to feet:
[tex]\[ \frac{1 \text { foot }}{12 \text { inches }} \][/tex]
Now, doing this multiplication cancels out the inches unit and leaves you with feet per minute:
[tex]\[ \frac{100 \text { inches }}{1 \text { minute }} \times \frac{1 \text { foot }}{12 \text { inches }} \][/tex]
Simplifying this multiplication:
[tex]\[ \frac{100}{1} \times \frac{1}{12} = \frac{100}{12} \][/tex]
[tex]\[ \frac{100}{12} = 8.333333333333332 \][/tex]
So, the correct expression for converting 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]
Therefore, the correct choice is:
[tex]\[ \frac{100 \text{ inches }}{1 \text{ minute }} \times \frac{1 \text{ foot }}{12 \text{ inches }}. \][/tex]
