1. **State the problem:** We are given the average time $58.2$ seconds for running $400$ meters, and the times vary by $6.4$ seconds from this average. We need to write an equation to find $t$, the maximum and minimum times. 2. **Write the general form of the equation:** The maximum and minimum times vary by $6.4$ seconds from the average, so we use: $$t - 58.2 = \pm 6.4$$ This means: $$t - 58.2 = 6.4 \quad \text{or} \quad t - 58.2 = -6.4$$ 3. **Solve for $t$ in each case:** For the maximum time: $$t - 58.2 = 6.4$$ Add $58.2$ to both sides: $$t = 6.4 + 58.2$$ $$t = 64.6$$ For the minimum time: $$t - 58.2 = -6.4$$ Add $58.2$ to both sides: $$t = -6.4 + 58.2$$ $$t = 51.8$$ 4. **Final answer:** The maximum time is $64.6$ seconds and the minimum time is $51.8$ seconds. Thus, the equation to find $t$ is: $$t - 58.2 = \pm 6.4$$ and the solutions are: $$t = 64.6, \quad t = 51.8$$