1. **State the problem:** Greg rows at 2 1/2 miles per hour in still water. It takes the same time to row 3 miles upstream and 4 1/2 miles downstream. We need to find the rate of the current. 2. **Define variables:** Let $c$ be the rate of the current in miles per hour. 3. **Write expressions for effective speeds:** - Upstream speed = $2.5 - c$ - Downstream speed = $2.5 + c$ 4. **Write the time equations:** - Time upstream = $\frac{3}{2.5 - c}$ - Time downstream = $\frac{4.5}{2.5 + c}$ Since times are equal: $$\frac{3}{2.5 - c} = \frac{4.5}{2.5 + c}$$ 5. **Solve the equation:** Cross multiply: $$3(2.5 + c) = 4.5(2.5 - c)$$ Expand: $$7.5 + 3c = 11.25 - 4.5c$$ Bring variables to one side: $$3c + 4.5c = 11.25 - 7.5$$ $$7.5c = 3.75$$ Divide both sides by 7.5: $$c = \frac{3.75}{7.5}$$ Show cancellation: $$c = \frac{\cancel{3.75}}{\cancel{7.5}} \times \frac{1}{2} = 0.5$$ 6. **Interpretation:** The rate of the current is 0.5 miles per hour. **Final answer:** $$\boxed{0.5 \text{ miles per hour}}$$