1. **State the problem:** A satellite travels 350 kilometers in 56 seconds. We want to find how far it travels in 8 seconds at the same rate. 2. **Set up the proportion:** Let $d$ be the distance traveled in 8 seconds. Since the rate is constant, the ratio of distance to time is the same for both cases. So, we write the proportion: $$\frac{350}{56} = \frac{d}{8}$$ 3. **Cross multiply to solve for $d$:** $$350 \times 8 = 56 \times d$$ 4. **Calculate the left side:** $$2800 = 56d$$ 5. **Divide both sides by 56 to isolate $d$:** $$\frac{2800}{\cancel{56}} = \frac{56d}{\cancel{56}}$$ $$50 = d$$ 6. **Final answer:** The satellite travels **50 kilometers** in 8 seconds at the same rate.