To find the farthest distance the one long hose can reach, we need to add the lengths of all three hoses together.
The lengths of the hoses are:
- Brown hose: 10.75 feet
- Green hose: 19.4 feet
- Black hose: 7.5 feet
Now, let's add these lengths together:
\[ 10.75 + 19.4 + 7.5 \]
Calculating step-by-step:
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Adding the brown and green hose: \[ 10.75 + 19.4 = 30.15 \text{ feet} \]
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Now adding the black hose to this total: \[ 30.15 + 7.5 = 37.65 \text{ feet} \]
Therefore, the farthest distance the one long hose can reach is
\[ \boxed{37.65} \text{ feet}. \]