1. **State the problem:** We know a satellite travels 70 kilometers in 8 seconds. We want to find the time $t$ it takes to travel 630 kilometers at the same rate. 2. **Set up the proportion:** Since distance and time are directly proportional at constant speed, we can write: $$\frac{t}{8} = \frac{630}{70}$$ Here, $t$ is the unknown time for 630 km, 8 is the time for 70 km, 630 is the new distance, and 70 is the original distance. 3. **Solve the proportion:** Cross multiply: $$t \times 70 = 8 \times 630$$ 4. **Simplify:** $$70t = 5040$$ 5. **Isolate $t$ by dividing both sides by 70:** $$t = \frac{5040}{70}$$ Show cancelation: $$t = \frac{\cancel{70}72}{\cancel{70}1} = 72$$ 6. **Answer:** It takes the satellite 72 seconds to travel 630 kilometers at the same rate.