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. Find $x$ and $x+4$. 2. **Recall the formula:** Time = Distance \div Speed. 3. **Write expressions for their times:** - Matthew's time: $\frac{x}{12}$ hours - Zoe's time: $\frac{x+4}{10}$ hours 4. **Set up the equation for total time:** $$\frac{x}{12} + \frac{x+4}{10} = 1.5$$ 5. **Find common denominator and solve:** Multiply both sides by 60 (LCM of 12 and 10): $$60 \times \left(\frac{x}{12} + \frac{x+4}{10}\right) = 60 \times 1.5$$ $$5x + 6(x+4) = 90$$ 6. **Simplify:** $$5x + 6x + 24 = 90$$ $$11x + 24 = 90$$ 7. **Isolate $x$:** $$11x = 90 - 24$$ $$11x = 66$$ 8. **Divide both sides by 11:** $$x = \frac{66}{11}$$ $$x = 6$$ 9. **Find Zoe's distance:** $$x + 4 = 6 + 4 = 10$$ **Final answer:** Matthew rode 6 km and Zoe rode 10 km.