相遇后再追及的数学问题

  • 时间:2020-05-31 15:41:53
  • 分类:数学世界
  • 阅读:142 次

小学数学群“怪盗”同学分享一道相遇后再追及的数学问题:快车和慢车同时从甲、乙两地相向而行,在离乙地120千米处相遇,相遇后两车继续按原速前进,快车到达乙地后立即返回,结果两车同时到达甲地。求甲、乙两地的路程。

数学题解答:此题看起来有些复杂,且题中条件很少。但仔细分析后,就会发现快车速度与慢车速度之间的关系:快车的速度是慢车的2倍。怎么想的呢?

请看下图:快车到达乙地后返回,而慢车继续向甲地前行,然后两车同时到达甲地。此时快车行了两地路程的2倍(即往返各一次),而慢车正好行了两地的路程,由此可见,快车速度是慢车的2倍。所以当两车在途中相遇时,慢车行了120千米,此时快车应该行了:120×2=240(千米),两车所行路程相加即为甲乙两地的距离:120+2470=360(千米)。还可以用这样的算式:120×(2+1)=360(千米),你能看懂它的意思吗?

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