1. **State the problem:** Two pairs, kids and adults, race with the kids starting 18 yards ahead. Kids move at 1 yard/second, adults at 2 yards/second. We want to find how far the adults run and how long it takes for them to catch the kids. 2. **Define variables:** Let $t$ be the time in seconds after the start when adults catch the kids. Let $d$ be the distance in yards the adults run in time $t$. 3. **Write equations:** Kids start 18 yards ahead and move at 1 yard/second, so their position after $t$ seconds is: $$\text{Kids position} = 18 + 1 \times t = 18 + t$$ Adults start at 0 and move at 2 yards/second, so their position after $t$ seconds is: $$\text{Adults position} = 2 \times t = 2t$$ 4. **Set positions equal to find when adults catch kids:** $$18 + t = 2t$$ 5. **Solve for $t$:** $$18 = 2t - t$$ $$18 = t$$ 6. **Find distance adults ran:** $$d = 2t = 2 \times 18 = 36$$ 7. **Answer:** The adults ran 36 yards and caught up to the kids in 18 seconds.