1.1 速度·路程·时间 Speed, Distance, Time
路程、速度、时间三者之间的关系，是行程问题的核心：
The relationship between distance, speed, and time is the foundation of motion problems:
Watch units! Mix-ups between km/h and m/s are the most common error in rate problems!
1.2 相遇与追及 Meeting and Chasing Problems
相遇问题：两个物体相向而行，相遇时：
Meeting problems: Two objects moving toward each other:
追及问题：两个物体同向而行，后者追上前者时：
Chasing problems: Two objects moving in the same direction:
2.1 工作量·效率·时间 Work, Rate, Time
工程问题的结构与行程问题完全对称：
Work problems have the exact same structure as motion problems:
通常设工作总量为 1（单位工作量）。如果某人单独完成工作需要 n 小时，则其工作效率 = 1/n。
Usually set total work = 1 (one unit). If someone finishes alone in n hours, their work rate = 1/n.
2.2 合作问题 Combined Work Problems
多人合作时，总效率 = 各人效率之和：
When multiple workers collaborate, total rate = sum of individual rates:
举例：甲单独完成工作需要6小时，乙需要3小时。两人合作需要多久？
甲效率 = 1/6，乙效率 = 1/3，总效率 = 1/6 + 1/3 = 1/2，合作时间 = 1 ÷ 1/2 = 2小时
Key trick: set total work = 1. Express each person's rate, then add them up.
3.1 流水行船 River Boat Problems
顺水（顺风）时：实际速度 = 船速 + 水速（风速）；逆水（逆风）时：实际速度 = 船速 − 水速（风速）。
Downstream: actual speed = boat speed + current speed. Upstream: actual speed = boat speed − current speed.
In river problems, first find the boat's speed and current speed from given info, then solve the rest.
一辆汽车以 60 km/h 的速度行驶了 2.5 小时，走了多少公里？A car travels at 60 km/h for 2.5 hours. How far does it go?
甲、乙两地相距360km，甲车速度80km/h，乙车速度100km/h，两车同时相向而行，几小时相遇？A and B are 360 km apart. Car A: 80 km/h. Car B: 100 km/h. They drive toward each other. When do they meet?
甲单独完成一项工作需要8天，乙单独需要12天。甲乙合作，需要多少天完成？A finishes a job in 8 days, B in 12 days. Working together, how many days?
总效率 = 1/8 + 1/12 = (3+2)/24 = 5/24
合作时间 = 1 ÷ 5/24 = 24/5 = 4.8天 Set W=1. A rate=1/8, B rate=1/12. Combined rate=5/24. Time=1÷5/24=24/5=4.8 days.
一条船在顺水中速度为20km/h，逆水中速度为12km/h。船在静水中的速度是？水速是？A boat goes 20 km/h downstream and 12 km/h upstream. What is its speed in still water? Current speed?
逆水速度 = 船速 − 水速 = 12
两式相加：2×船速 = 32 → 船速 = 16 km/h
水速 = 20 − 16 = 4 km/h v_down + v_up = 2×v_boat → v_boat = 16 km/h. v_water = 20 − 16 = 4 km/h.
甲以5km/h先行2小时，乙以15km/h追赶。乙几小时后追上甲？A walks at 5 km/h, starts 2 hours early. B chases at 15 km/h. When does B catch up?
乙追上时：速度差 = 15−5 = 10 km/h
追及时间 = 距离差 ÷ 速度差 = 10 ÷ 10 = 1小时 A gets 10 km head start (5×2). Speed difference = 15−5 = 10 km/h. Time = 10/10 = 1 hour.
第1题 某人以8km/h的速度走了3小时，一共走了多少公里？A person walks at 8 km/h for 3 hours. How far?
第2题 甲、乙两人相距240m，同时相向而行，速度分别是3m/s和5m/s，几秒后相遇？A and B are 240m apart, walking toward each other at 3 m/s and 5 m/s. When do they meet?
第3题 甲单独完成工作需要10小时，乙需要15小时。合作需要多少小时？A finishes in 10h, B in 15h. Together in how many hours?
第4题 一条船顺水速度为18km/h，逆水速度为10km/h。静水中船速是多少？Downstream 18 km/h, upstream 10 km/h. Speed in still water?
第5题 甲先走4km后，乙开始以12km/h追赶。甲速度6km/h，乙几小时追上？A walks 4 km first, then B chases at 12 km/h while A walks at 6 km/h. When does B catch A?
第6题 两地相距200km，甲车60km/h，乙车40km/h，相向而行，2小时后两车相距多少？200 km apart. Car A: 60 km/h, Car B: 40 km/h, drive toward each other for 2 hours. How far apart?
第7题 小明以5km/h的速度走了120分钟，一共走了多少米？Xiao Ming walks at 5 km/h for 120 minutes. How many meters?
第8题 某工人单独完成工作需要20天，他的效率是多少？（设工作总量为1）A worker finishes alone in 20 days. What is their work rate? (W=1)