1. **State the problem:** Jamal rides 6 miles downhill to the skate park and returns uphill on the same trail. His uphill speed is 1 mile per hour slower than his downhill speed. The return trip takes 1 hour longer than the trip to the park. We need to find his downhill speed. 2. **Define variables:** Let $d$ be the downhill speed in miles per hour. 3. **Write expressions for time:** - Time downhill = distance / speed = $\frac{6}{d}$ hours - Uphill speed = $d - 1$ miles per hour - Time uphill = $\frac{6}{d - 1}$ hours 4. **Set up the equation using the time difference:** $$\frac{6}{d - 1} - \frac{6}{d} = 1$$ 5. **Solve the equation:** Multiply both sides by $d(d - 1)$ to clear denominators: $$6d - 6(d - 1) = d(d - 1)$$ Simplify left side: $$6d - 6d + 6 = d^2 - d$$ Which reduces to: $$6 = d^2 - d$$ Rewrite as a quadratic equation: $$d^2 - d - 6 = 0$$ 6. **Factor the quadratic:** $$(d - 3)(d + 2) = 0$$ 7. **Find the roots:** $d = 3$ or $d = -2$ 8. **Choose the valid speed:** Speed cannot be negative, so $d = 3$ miles per hour. **Final answer:** Jamal's downhill speed is $\boxed{3}$ miles per hour.