1. **State the problem:** We have two days with jogging and walking times and total distances. We want to find the relationship between jogging and walking speeds. 2. **Define variables:** Let $x$ be the jogging speed in miles per minute and $y$ be the walking speed in miles per minute. 3. **Write equations from the data:** - Saturday: jogging time = 15 min, walking time = 30 min, total distance = 3.5 mi $$15x + 30y = 3.5$$ - Sunday: jogging time = 60 min (1 h), walking time = 30 min, total distance = 8 mi $$60x + 30y = 8$$ 4. **Simplify equations:** - Saturday: divide by 15 $$x + 2y = \frac{3.5}{15} = 0.2333$$ - Sunday: divide by 30 $$2x + y = \frac{8}{30} = 0.2667$$ 5. **Solve the system:** From Saturday: $$x = 0.2333 - 2y$$ Substitute into Sunday: $$2(0.2333 - 2y) + y = 0.2667$$ $$0.4667 - 4y + y = 0.2667$$ $$-3y = 0.2667 - 0.4667 = -0.2$$ $$y = \frac{0.2}{3} = 0.0667$$ 6. **Find jogging speed:** $$x = 0.2333 - 2(0.0667) = 0.2333 - 0.1334 = 0.0999$$ 7. **Interpretation:** - Jogging speed $x \approx 0.1$ miles per minute (6 miles per hour) - Walking speed $y \approx 0.067$ miles per minute (4 miles per hour) These speeds explain the total distances covered on both days given the times jogging and walking.