1. **Problem statement:** Two points A and B are 1200 km apart. They start moving towards each other at the same time and meet in 24 hours. If A starts 10 hours after B, they meet 20 hours after A starts. Find their speeds. 2. **Define variables:** Let speed of A be $v_A$ km/h and speed of B be $v_B$ km/h. 3. **First scenario (both start together):** They meet after 24 hours, so the sum of distances covered by A and B equals 1200 km: $$v_A \times 24 + v_B \times 24 = 1200$$ Simplify: $$24(v_A + v_B) = 1200$$ $$v_A + v_B = \frac{1200}{24} = 50$$ 4. **Second scenario (A starts 10 hours late):** B starts first and travels for $10 + 20 = 30$ hours, A starts after 10 hours and travels for 20 hours. They meet after 20 hours from A's start. Distance covered by A: $$v_A \times 20$$ Distance covered by B: $$v_B \times 30$$ Sum of distances equals 1200 km: $$20 v_A + 30 v_B = 1200$$ Divide entire equation by 10: $$2 v_A + 3 v_B = 120$$ 5. **Solve the system of equations:** From step 3: $$v_A + v_B = 50$$ Express $v_A$: $$v_A = 50 - v_B$$ Substitute into step 4: $$2(50 - v_B) + 3 v_B = 120$$ $$100 - 2 v_B + 3 v_B = 120$$ $$100 + v_B = 120$$ $$v_B = 20$$ 6. **Find $v_A$:** $$v_A = 50 - 20 = 30$$ **Answer:** Speed of A is 30 km/h and speed of B is 20 km/h.