1. **State the problem:** We are given a cost of 176 for 11 hours and want to find the cost for 374 hours using proportions. 2. **Formula used:** The unit rate is calculated as cost per hour: $$\text{Unit rate} = \frac{176}{11}$$ 3. **Calculate the unit rate:** $$\frac{176}{11} = 16$$ 4. **Use the unit rate to find the cost for 374 hours:** $$\text{Cost} = 16 \times 374$$ 5. **Calculate the total cost:** $$16 \times 374 = 5984$$ 6. **Answer:** The cost for 374 hours is 5984.