1. **State the problem:** A jet travels 4488 miles against the wind in 8 hours and 5368 miles with the wind in 8 hours. We need to find the rate of the jet in still air ($j$) and the rate of the wind ($w$). 2. **Set up variables and equations:** Let $j$ = rate of the jet in still air (mi/h), and $w$ = rate of the wind (mi/h). 3. **Write the equations based on the problem:** - Against the wind, the effective speed is $j - w$. - With the wind, the effective speed is $j + w$. Using distance = speed × time: $$4488 = (j - w) \times 8$$ $$5368 = (j + w) \times 8$$ 4. **Simplify the equations:** Divide both equations by 8: $$j - w = \frac{4488}{8} = 561$$ $$j + w = \frac{5368}{8} = 671$$ 5. **Solve the system of equations:** Add the two equations: $$ (j - w) + (j + w) = 561 + 671 $$ $$ 2j = 1232 $$ $$ j = \frac{1232}{2} = 616 $$ Substitute $j=616$ into $j + w = 671$: $$ 616 + w = 671 $$ $$ w = 671 - 616 = 55 $$ 6. **Answer:** - Rate of the jet in still air is $\boxed{616}$ mi/h. - Rate of the wind is $\boxed{55}$ mi/h. This means the jet flies at 616 miles per hour in still air, and the wind speed is 55 miles per hour.