To determine whether Melanie can water her vegetables, we need to find the total length of the hoses when connected together. We can do this by adding the lengths of the three hoses:
- Brown hose: 10.75 feet
- Green hose: 19.4 feet
- Black hose: 7.5 feet
Now, we add them together:
\[ 10.75 + 19.4 + 7.5 = 37.65 \text{ feet} \]
Now we compare the total length of the hoses (37.65 feet) to the distance to the vegetable garden (30 feet):
Since 37.65 feet is greater than 30 feet, Melanie will be able to water her vegetables.