1. **Problem:** Solve the system of equations from Bài 3: Two cyclists start simultaneously from two cities 38 km apart, moving towards each other. They meet after 2 hours. The first cyclist has traveled 2 km more than the second when they meet. Find their speeds. 2. **Formula and rules:** - Let $v_1$ and $v_2$ be the speeds of the first and second cyclist respectively. - Distance = Speed $\times$ Time. - Since they meet after 2 hours, the sum of distances they travel is 38 km. - The first cyclist travels 2 km more than the second: $d_1 = d_2 + 2$. 3. **Set up equations:** - $d_1 + d_2 = 38$ - $d_1 = d_2 + 2$ - Since $d_1 = v_1 \times 2$ and $d_2 = v_2 \times 2$, substitute: $$2v_1 + 2v_2 = 38$$ $$2v_1 = 2v_2 + 2$$ 4. **Simplify equations:** - Divide the first equation by 2: $$\cancel{2}v_1 + \cancel{2}v_2 = 38 \Rightarrow v_1 + v_2 = 19$$ - Divide the second equation by 2: $$\cancel{2}v_1 = \cancel{2}v_2 + 2 \Rightarrow v_1 = v_2 + 1$$ 5. **Substitute $v_1$ in the first equation:** $$(v_2 + 1) + v_2 = 19$$ $$2v_2 + 1 = 19$$ $$2v_2 = 18$$ $$v_2 = 9$$ 6. **Find $v_1$:** $$v_1 = v_2 + 1 = 9 + 1 = 10$$ 7. **Answer:** - The first cyclist's speed is $10$ km/h. - The second cyclist's speed is $9$ km/h. --- 1. **Problem:** Solve the problem from Bài 4: A car travels on segment AB at 50 km/h, then on segment BC at 45 km/h. The total distance AB + BC = 165 km. The time on AB is 30 minutes less than the time on BC. Find the time spent on each segment. 2. **Formula and rules:** - Let $t_1$ and $t_2$ be the times spent on AB and BC respectively (in hours). - Distance = Speed $\times$ Time. - Total distance: $50t_1 + 45t_2 = 165$ - Time difference: $t_2 - t_1 = 0.5$ (30 minutes = 0.5 hours) 3. **Set up equations:** $$50t_1 + 45t_2 = 165$$ $$t_2 - t_1 = 0.5$$ 4. **Express $t_2$ from second equation:** $$t_2 = t_1 + 0.5$$ 5. **Substitute into first equation:** $$50t_1 + 45(t_1 + 0.5) = 165$$ $$50t_1 + 45t_1 + 22.5 = 165$$ $$95t_1 + 22.5 = 165$$ $$95t_1 = 165 - 22.5 = 142.5$$ $$t_1 = \frac{142.5}{95} = 1.5$$ 6. **Find $t_2$:** $$t_2 = 1.5 + 0.5 = 2$$ 7. **Answer:** - Time on AB is 1.5 hours. - Time on BC is 2 hours.