1. **Problem statement:** Corey travels to the fitness centre on Saturday and Sunday with different average speeds and arrival times. We want to express the Sunday travel time in terms of $t$, the Saturday travel time, and then form an equation to find $t$. 2. **Given:** - Saturday speed = 30 km/h = 0.5 km/min - Sunday speed = 36 km/h = 0.6 km/min - Saturday arrival: 2 minutes late - Sunday arrival: 4 minutes early - Saturday travel time = $t$ minutes 3. **(a) Expression for Sunday travel time:** Since Corey was 2 minutes late on Saturday and 4 minutes early on Sunday, the difference in travel times is 6 minutes. Therefore, Sunday travel time = $t - 6$ minutes. 4. **(b) Forming the equation:** Distance travelled is the same both days. Distance on Saturday = speed $\times$ time = $0.5t$ km Distance on Sunday = $0.6(t - 6)$ km Set equal: $$0.5t = 0.6(t - 6)$$ 5. **Solving the equation:** $$0.5t = 0.6t - 3.6$$ Subtract $0.6t$ from both sides: $$0.5t - 0.6t = -3.6$$ $$\cancel{0.5}t - \cancel{0.6}t = -3.6$$ $$-0.1t = -3.6$$ Divide both sides by $-0.1$: $$t = \frac{-3.6}{-0.1} = 36$$ 6. **Final answer:** Corey took $t = 36$ minutes to travel on Saturday. Note: The user’s provided solution had $t=3.27$ which seems inconsistent with the units and problem context; the correct solution is $t=36$ minutes.