To solve the given optimization problem using Gurobi, we first need to understand and translate the natural language description into a mathematical formulation. The objective is to minimize a linear function of the hours worked by three individuals (Hank, Jean, and Mary) subject to several constraints involving their organization scores and relationships between their working hours.

Let's denote:
- \(x_0\) as the hours worked by Hank,
- \(x_1\) as the hours worked by Jean,
- \(x_2\) as the hours worked by Mary.

The objective function to minimize is: 
\[6.35x_0 + 4.82x_1 + 7.75x_2\]

Given constraints:
1. Organization score constraints for each individual are not directly limiting but are part of combined constraints.
2. \(5.9x_0 + 20.41x_2 \geq 87\)
3. \(5.9x_0 + 19.39x_1 \geq 61\)
4. \(5.9x_0 + 19.39x_1 + 20.41x_2 \geq 61\)
5. \(-10x_0 + 6x_2 \geq 0\)
6. \(7x_1 - 9x_2 \geq 0\)
7. \(5.9x_0 + 19.39x_1 \leq 175\)

All variables (\(x_0, x_1, x_2\)) are continuous (can be fractional).

Here is the Gurobi code to solve this problem:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
hours_worked_by_Hank = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Hank")
hours_worked_by_Jean = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Jean")
hours_worked_by_Mary = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Mary")

# Define the objective function
m.setObjective(6.35*hours_worked_by_Hank + 4.82*hours_worked_by_Jean + 7.75*hours_worked_by_Mary, GRB.MINIMIZE)

# Add constraints
m.addConstr(5.9*hours_worked_by_Hank + 20.41*hours_worked_by_Mary >= 87, name="organization_score_min_1")
m.addConstr(5.9*hours_worked_by_Hank + 19.39*hours_worked_by_Jean >= 61, name="organization_score_min_2")
m.addConstr(5.9*hours_worked_by_Hank + 19.39*hours_worked_by_Jean + 20.41*hours_worked_by_Mary >= 61, name="total_organization_score_min")
m.addConstr(-10*hours_worked_by_Hank + 6*hours_worked_by_Mary >= 0, name="hank_mary_constraint")
m.addConstr(7*hours_worked_by_Jean - 9*hours_worked_by_Mary >= 0, name="jean_mary_constraint")
m.addConstr(5.9*hours_worked_by_Hank + 19.39*hours_worked_by_Jean <= 175, name="organization_score_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Hank: {hours_worked_by_Hank.x}")
    print(f"Hours worked by Jean: {hours_worked_by_Jean.x}")
    print(f"Hours worked by Mary: {hours_worked_by_Mary.x}")
else:
    print("No optimal solution found")
```