甲、乙两辆清洁车执行东、西城间的公路清扫任务.甲车单独清扫需要10小时,乙车单独清扫需要15小时,两车同时从东、西城相向开出,相遇时甲车比乙车多清扫12千米,问东、西两城相距多少千米?
解:根据题意可得:甲车的速度为:
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,乙车速度为:
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,
1÷(
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+
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)
=1÷
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=1×6
=6(小时);
12÷(
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×6
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)
=12÷(
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)
=12÷
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=12×5
=60(千米);
答:两城相距60千米.
分析:把总路程看做单位“1”,由题干可知,甲车的速度为:
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,乙车速度为:
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,求得相遇时间,进一步求出甲车比乙车多清扫的占总路程的几分之几,并由此列式解决问题.
点评:抓住题干,找出甲乙两车的速度,从而计算出它们共同使用的时间,是解决本题的关键.