大客车与小客车同时从A市出发到B市,客车每小时行驶90千米,小汽车第一小时行驶60千米,以后每小时增加5千米

大客车与小客车同时从A市出发到B市,客车每小时行驶90千米,小汽车第一小时行驶60千米,以后每小时增加5千米,小汽车需要()小时追上客车?要算式和解释。... 大客车与小客车同时从A市出发到B市,客车每小时行驶90千米,小汽车第一小时行驶60千米,以后每小时增加5千米,小汽车需要( )小时追上客车?

要算式和解释。
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(30/5)*2+1=13小时
解释,第一小时大客车比小汽车快30千米,因小汽车每小时增加5千米,那么到(30/5)+1=7小时时,两车速度相等,那么要再经过30/5=6小时时小客车的速度比大客车快30千米,故小汽车需要( 13 )小时追上客车
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设X小时追上,此时:

客车行驶距离为:90X千米;

小客车行驶距离:60+(60+5)+(60+5*2)+。。。+(60+5*(X-1))=60X+5*(1+(X-1))/2 =60X+2.5X*(X-1)

二者距离相等,所以:90X=60X+2.5X*(X-1)
整理得:2.5(X-1)=30
解得:X=13
即,13小时后追上。
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(30/5)*2+1=13小时 解释,第一小时大客车比小汽车快30千米,因小汽车每小时增加5千米,那么到(30/5)+1=7小时时,两车速度相等,那么要再经过30/5=6小时时小客车的速度比大客车快30千米,故小汽车需要( 13 )小时追上客车
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13个小时

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