一道英数题Two ants start at point A and walk at the same pace. On
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一道英数题
Two ants start at point A and walk at the same pace. One ant walks around a 3 cm by 3 cm square whilst the other walks around a 6 cm by 3 cmrectangle. What is the minimum distance, in centimetres, any one mustcover before they meet again?
Two ants start at point A and walk at the same pace. One ant walks around a 3 cm by 3 cm square whilst the other walks around a 6 cm by 3 cmrectangle. What is the minimum distance, in centimetres, any one mustcover before they meet again?
我忘记上传图了
翻译:两只蚂蚁从A点开始用相同速度移动,一只蚂蚁走3cm*3cm正方形路线,另一只走6cm*3cm矩形(矩形的单词打错咯~).如果两只蚂蚁要相遇,它们至少走过多少路程?
解法:
首先想象这样一个地形:日
两只蚂蚁同时从“日”右上角出发,顺时针旋转,但一只蚂蚁走小口,一只蚂蚁走大口.两个蚂蚁经过每一小直线的速度一样.用两个手指当作两个蚂蚁,慢慢画圈,看什么时候两个手指会到同一点就行了.画画就能看出来,走过30cm(也就是走小口的蚂蚁绕了两圈半),两只蚂蚁相遇.
英语答案的话这样写:The answer is 30cm.
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那么上面的解法就完全错了.
稍微改动下:把两个手指放在A点,按两个蚂蚁的方式转动,第二个蚂蚁走长边时第一个蚂蚁走两条边,转一转就能转出来了,第一个蚂蚁走三圈时第二个蚂蚁正好走两圈,都在A点.答案是36cm
The answer is 36cm.
PS:专业一点的解法:两个蚂蚁相遇,也就是他们都经过了整数圈(因为整数圈后在A点).小正方形周长12cm,大矩形周长18cm,找12和18的最小公倍数,也就是36
解法:
首先想象这样一个地形:日
两只蚂蚁同时从“日”右上角出发,顺时针旋转,但一只蚂蚁走小口,一只蚂蚁走大口.两个蚂蚁经过每一小直线的速度一样.用两个手指当作两个蚂蚁,慢慢画圈,看什么时候两个手指会到同一点就行了.画画就能看出来,走过30cm(也就是走小口的蚂蚁绕了两圈半),两只蚂蚁相遇.
英语答案的话这样写:The answer is 30cm.
---------
那么上面的解法就完全错了.
稍微改动下:把两个手指放在A点,按两个蚂蚁的方式转动,第二个蚂蚁走长边时第一个蚂蚁走两条边,转一转就能转出来了,第一个蚂蚁走三圈时第二个蚂蚁正好走两圈,都在A点.答案是36cm
The answer is 36cm.
PS:专业一点的解法:两个蚂蚁相遇,也就是他们都经过了整数圈(因为整数圈后在A点).小正方形周长12cm,大矩形周长18cm,找12和18的最小公倍数,也就是36
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