题目与解析
问题
甲、乙两人在同一条椭圆形跑道上做特殊训练。他们同时从同一地点出发,沿相反方向跑。每人跑完第一圈到达出发点后,立即回头加速跑第二圈,跑第一圈时,乙的速度是甲的3,甲跑第二圈时的速度比第一圈提高了3,乙跑第二圈时速度提高了5。已知甲、乙两人第二次相遇点距第一次相遇点190米。这条椭圆形跑道长多少米?
答案与解析
根据题意画图34-2:甲、乙从A点出发,沿相反方向跑,他们的速度比是1:
3=3:2。第一次相遇时,他们所行路程比是3:2,把全程平均分成5份,则他们第一次相遇点在B点。当甲A点时,乙又行了2÷3×2=1
3。这时甲反西肮
而行,速度提高了
3。甲、乙速度比为[3×(1+
3):2]=2:1,当乙到达A点时,甲反向行了(3—1
3)×2=3
3。这时乙反向而行,甲、乙的速度比变成了[3×(1+
3)]:[2×(1+
5)]=5:3。这样,乙又行了(5—3
3)×
5+3=
8,与甲在C点相遇。B、C的路程为190米,对应的份数为3—
8=2
8。列式为1:
3=3:2 2÷3×2=1
3[3×(1+
3):2]=2:1 (3—1
3)×2=3
3 [3×(1+
3)]:[2×(1+
5)]=5:3
(5—3
3)×
5+3=
8 190÷(3-
8)×5=400(米)
答:这条椭圆形跑道长400米。
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