1. **Problem Statement:** Jacob spends 60 minutes in the gym doing freehand exercises and running on the treadmill. He runs on the treadmill for 30 minutes longer than he does freehand exercises. 2. **Define variables:** Let $y$ be the number of minutes Jacob does freehand exercises. Let $x$ be the number of minutes Jacob runs on the treadmill. 3. **Write equations:** - Total time spent is 60 minutes: $$x + y = 60$$ - Running time is 30 minutes longer than freehand exercises: $$x = y + 30$$ 4. **Part A answer:** The pair of linear equations is: $$\begin{cases} x + y = 60 \\ x = y + 30 \end{cases}$$ 5. **Part B: Find $y$ (freehand exercise time):** Substitute $x = y + 30$ into $x + y = 60$: $$ (y + 30) + y = 60 $$ $$ 2y + 30 = 60 $$ Subtract 30 from both sides: $$ 2y + \cancel{30} - \cancel{30} = 60 - 30 $$ $$ 2y = 30 $$ Divide both sides by 2: $$ \frac{2y}{\cancel{2}} = \frac{30}{\cancel{2}} $$ $$ y = 15 $$ Jacob spends 15 minutes doing freehand exercises. 6. **Part C: Is it possible Jacob runs 40 minutes?** If $x = 40$, then from $x = y + 30$: $$ 40 = y + 30 $$ $$ y = 40 - 30 = 10 $$ Total time would be: $$ x + y = 40 + 10 = 50 $$ This is less than 60 minutes, so it is **not possible** for Jacob to run 40 minutes and spend exactly 60 minutes total while running 30 minutes longer than freehand exercises. **Final answers:** - Part A: $$\begin{cases} x + y = 60 \\ x = y + 30 \end{cases}$$ - Part B: $$y = 15$$ minutes - Part C: No, it is not possible.