1. **State the problem:** Ellie and Colette are typing research papers. Ellie types 1 page per hour and already has 15 pages done. Colette types 3 pages per hour and has 3 pages done. We want to find how long it takes for them to have the same number of pages typed and what that page count will be. 2. **Define variables:** Let $t$ be the number of hours after they start typing together. 3. **Write expressions for their page counts after $t$ hours:** - Ellie: $15 + 1 \times t = 15 + t$ - Colette: $3 + 3 \times t = 3 + 3t$ 4. **Set their page counts equal to find $t$:** $$15 + t = 3 + 3t$$ 5. **Solve for $t$:** $$15 + t = 3 + 3t$$ $$15 - 3 = 3t - t$$ $$12 = 2t$$ $$t = \frac{12}{2} = 6$$ 6. **Find the page count at that time:** Substitute $t=6$ into Ellie's or Colette's expression: $$15 + 6 = 21$$ or $$3 + 3 \times 6 = 3 + 18 = 21$$ **Answer:** After 6 hours, both Ellie and Colette will have typed 21 pages.