行程问题

考什么 · What it tests

需要先会 · Prerequisites

• 一元一次方程（设未知数） / One-variable linear equations
• 单位换算（分钟↔小时） / Unit conversion (minutes ↔ hours)
• 比与比例 / Ratios and proportions

常见套路 · Common moves

1. 相遇看速度和、追及看速度差：把两个运动的人合成一个「相对速度」，双人问题立刻变成单人问题。

   Meetings use the sum of speeds, chases use the difference: merge two movers into one "relative speed" and a two-person problem becomes a one-person problem.
2. 平均速度 = 总路程 ÷ 总时间，不是两个速度取平均：去 30 回 60，平均是 40 不是 45——它永远偏向慢的那段。这是四五星双解里的高频巧解点。

   Average speed = total distance ÷ total time, not the average of the two speeds: going at 30 and returning at 60 averages 40, not 45 — it always leans toward the slower leg. A frequent shortcut in 4–5★ solutions.
3. 多段变速先画线段图：把出发、转折、相遇各事件标上时间和位置，方程会自己从图里浮出来。

   For multi-stage trips, draw a segment diagram first: mark each event's time and position, and the equation surfaces on its own.

易错点 · Common pitfalls

• 单位不统一就代公式：速度是每小时、时间给的是分钟，先换算再计算。

  Plugging in mismatched units: speed per hour but time in minutes — convert before you compute.
• 「平均速度=两速度的平均数」是出题人必设的陷阱选项，看到「来回/往返」先警觉。

  "Average speed = mean of the two speeds" is a trap choice the writers always plant — the words "round trip" should raise your guard.