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2020年國考行測數量關系行程問題之相遇追及

公考資料網 2019/08/08 11:39:06

  歷年行測數量關系題是很多人望而卻步的一塊內容,其實我們如果能把每個知識點一個一個學明白,數學也沒我們想象的那么難。而數量的題目當中,行程問題的難度當排在首位了,每年的出題人也特別愛出行程問題,今天公考資料網(http://www.btdfsx.com/)就教你來把這塊硬骨頭啃下一塊來。

  

  行程當中的相遇追及問題相信大家都有所耳聞,下面我們先來回顧一下基本概念和公式。

  

  對于相遇問題來說,題目的先設條件一般是甲乙兩人同時從A、B兩地出發相向而行,最終在AB路段的某一點C相遇,那么在這個過程當中,甲乙的初始距離AB段其實就是我們耳熟能詳的相遇路程了,這段路程其實是由甲乙兩人共同走完的,它等于甲走的路程AC加上乙走的路程BC,因此我們又把相遇路程叫做路程和。而甲乙兩人所走的路程實際上就等于兩人各自的速度乘以時間,這個時間也就是相遇時間,所以我們就得到了相遇路程的公式:

  

  AB= V甲×t+V乙×t=( V甲+V乙)×t

  

  總結起來也就是路程和=速度和×相遇時間

  

  對于追及問題來說,題目的先設條件一般是甲乙兩人同時從A、B兩地出發同向而行,最終甲在B點之后的某一點C追上了乙,那么相似的,甲乙的初始距離AB段在此時就是追及路程,甲同樣還是走了AC段,乙走了BC段,那在追及的問題中甲是比乙多走了AB這段路程的,AB等于AC減去BC,因此我們把追及路程叫做路程差。同樣通過路程和速度時間的關系我們可以得到:

  

  AB= V甲×t — V乙×t=(V甲 — V乙)×t

  

  t表示的是同時出發后甲追上乙所用的時間,總結起來就是路程差=速度差×追及時間

  

  那么相遇和追及問題的公式我們已經講明白了,下面就來看一下相遇追及的題目會不會做呢?

  

  例題1.已知A、B兩地相距600千米。甲、乙兩車同時從A、B兩地出發相向而行,3小時相遇。若甲的速度是乙的1.5倍,則甲的速度是( )千米/小時?

  

  A.60   B.80   C.90   D.120

  

  【答案】D。解析:已知路程和AB=600千米,相遇時間為3小時,可知V甲+V乙=路程和÷時間=600÷3=200千米,又知甲速度是乙速度的1.5倍,因此V乙=200÷(1+1.5)=80,故V甲=80×1.5=120。

  

  例題2.一只獵豹鎖定了距離自己200米遠的一只羚羊,以108千米/小時的速度發起進攻,2秒鐘后,羚羊意識到危險,以72千米/小時的速度快速逃命。問獵豹捕捉到羚羊時,羚羊跑了多少路程?

  

  A.520米   B.360米   C.280米   D.240米

  

  【答案】C。解析:選項單位是米,因此我們先統一單位。獵豹速度108千米/小時=30米/秒,羚羊速度72千米/小時=20米/秒。由于獵豹先跑了2秒羚羊才開始跑,此時才算開始追及,所以路程差=200-2×30=140米,則追及時間=路程差÷速度差=140÷(30-20)=14秒,即羚羊跑了14秒,所以羚羊的路程=速度×時間=20×14=280米。

  

  通過以上題目的練習,相遇追及的知識點大家是不是已經有所領會啦,當然還有更難一些的題目,但是萬變不離其宗,理解了路程和和路程差的公式,普通的相遇追及問題我們就可以把它拿下啦!公考資料網希望本篇對各位小伙伴有所幫助,祝大家學有所成,早日成公!

  

  學完理論知識后,想刷題提升可以下載必勝公考APP在線刷題,海量題目等你來刷。


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