1. **State the problem:** A barrel shaped like a cylinder with diameter 3.1 ft is rolled up a ramp 379 ft long. We need to find how many times the barrel turns. 2. **Formula used:** The number of turns is the total distance rolled divided by the circumference of the barrel's base. 3. **Calculate the circumference:** $$\text{Circumference} = \pi \times \text{diameter} = 3.14 \times 3.1 = 9.734 \text{ ft}$$ 4. **Calculate the number of turns:** $$\text{Number of turns} = \frac{\text{ramp length}}{\text{circumference}} = \frac{379}{9.734}$$ 5. **Intermediate step with cancellation:** $$\frac{\cancel{379}}{\cancel{9.734}} = 38.93$$ 6. **Round the answer:** The barrel turns approximately 38.9 times when rolled up the ramp. **Final answer:** $$\boxed{38.9}$$