1. **State the problem:** Matthew rides for $x$ km at 12 km/h. Zoe rides for $x+4$ km at 10 km/h. Their total riding time is 1.5 hours. We need to find $x$ and $x+4$. 2. **Formula:** Time taken = Distance \div Speed. 3. **Set up the equation:** Matthew's time = $\frac{x}{12}$ hours. Zoe's time = $\frac{x+4}{10}$ hours. Total time = $\frac{x}{12} + \frac{x+4}{10} = 1.5$. 4. **Solve the equation:** Multiply both sides by 60 (LCM of 12 and 10) to clear denominators: $$60 \times \left(\frac{x}{12} + \frac{x+4}{10}\right) = 60 \times 1.5$$ $$5x + 6(x+4) = 90$$ 5. **Simplify:** $$5x + 6x + 24 = 90$$ $$11x + 24 = 90$$ 6. **Isolate $x$:** $$11x = 90 - 24$$ $$11x = 66$$ $$x = \frac{66}{11}$$ 7. **Simplify fraction:** $$x = \cancel{\frac{66}{11}} = 6$$ 8. **Find Zoe's distance:** $$x + 4 = 6 + 4 = 10$$ **Answer:** Matthew rode 6 km and Zoe rode 10 km.