Final answer:
Ms. Bennett would take 1 and 7/8 hours to shovel the entire driveway based on the given proportion of her shoveling 2/5 of it in 3/4 of an hour.
Step-by-step explanation:
The student has asked how long it will take Ms. Bennett to shovel her entire driveway if she shoveled 2/5 of it in 3/4 of an hour. To find out, we can set up a proportion where we compare the part of the driveway shoveled to the total. Since 2/5 of the driveway takes 3/4 of an hour, the entire driveway, which is 5/5 (or 1 whole), would take:
\[ \frac{2}{5} \text{ driveway} : \frac{3}{4} \text{ hour} = \frac{5}{5} \text{ driveway} : x \text{ hours} \]
To solve for x, we can cross-multiply:
\[ 2 \cdot x = \frac{3}{4} \cdot 5 \]
\[ 2x = \frac{15}{4} \]
\[ x = \frac{15}{4} \cdot \frac{1}{2} \]
\[ x = \frac{15}{8} \]
\[ x = 1 \frac{7}{8} \text{ hours} \]
Therefore, it would take Ms. Bennett 1 and 7/8 hours to shovel the entire driveway.