数学关系答题技巧之火车过桥问题解题思路
火车过桥问题属于行程问题中的一类问题,特别之处就在于火车不等同于一个人,它本身具备一定的长度。当人过桥时,相当于是“点”在移动;火车过桥时,相当于“线”在移动,那么,“线”如何过桥呢?如图,显然,从线头(即火车车头)开始入桥,直到线尾(即火车车尾)出桥,才算一次完整的过桥。从中可得:火车移动的距离=桥长+车身长
因此,火车过桥问题中,路程=桥长+车身长
http://www.zzxingce.com/xingce/datijiqiao/shuliangguanxi/20140210/data:image/png;base64,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
例题1、一列长90米的火车以每秒30米的速度匀速通过一座长1200米的桥,所需时间为( )秒。
A、37
B、40
C、43
D、46
解析:根据题意可知,该题属于火车过桥问题,根据公式可知,火车的路程=1200+90=1290米,问题是求时间,根据“时间=路程÷速度”可得:t=1290÷30=43。故答案为C。
例题2、一列火车通过530米的桥需40秒钟,以同样的速度穿过380米的山洞需30秒钟。求这列火车的速度是每秒多少米?()b
A、10
B、15
C、20
D、25
解析:本题涉及了两次过桥,一次桥长是530米,一次桥长是380米,但车速一样,车也是同一辆车,也就是说车长没变。那么,设车长为s,设车速为v,根据“路程=速度×时间”分别可得::530+s=v*40, 380+s=v*30,解得:10v=530-380,v=15。故答案为B。
这两个题都是考查的最基本的火车过桥问题,难度并不大,但做题时不注意“车长”这个特殊因素的话,就特别容易做错,尤其初次备考行测的考友们,尤其需要注意!
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