1. **State the problem:** Akeem runs 1 mile each day for 7 days. His times for the first 6 days are 9.4, 9.0, 9.1, 8.9, 8.5, and 8.8 minutes. He wants his average running time over 7 days to be 9 minutes or less. We need to find the maximum time he can run on the 7th day to meet this goal. 2. **Write the formula for the mean:** The mean running time for 7 days is given by $$\text{mean} = \frac{\text{sum of all 7 times}}{7} \leq 9$$ 3. **Set up the inequality:** Let $x$ be the running time on the 7th day. Then $$\frac{9.4 + 9.0 + 9.1 + 8.9 + 8.5 + 8.8 + x}{7} \leq 9$$ 4. **Calculate the sum of the first 6 days:** $$9.4 + 9.0 + 9.1 + 8.9 + 8.5 + 8.8 = 53.7$$ 5. **Substitute and solve for $x$:** $$\frac{53.7 + x}{7} \leq 9$$ Multiply both sides by 7: $$\cancel{7} \times \frac{53.7 + x}{\cancel{7}} \leq 9 \times 7$$ $$53.7 + x \leq 63$$ 6. **Isolate $x$:** $$x \leq 63 - 53.7$$ $$x \leq 9.3$$ 7. **Interpretation:** The maximum running time Akeem can have on the last day to keep his average at 9 minutes or less is 9.3 minutes. **Final answer:** $$\boxed{9.3}$$ minutes