數難題 HEIP HELP HELP!!!

sausauma

數難題 HEIP HELP HELP!!!  
大雪後一天,小飛和爺爺一起測量一個圓形花圃的周長,他倆的起點和走的方向完全相同,小飛每步長48厘米,爺爺每步長72厘米,由於兩人腳印有重合,所以各走完一圈後雪地下只留下40個腳印,求花圃的周長?

     

sausauma

Anybody help! Tomorrow is deadline



        

freddielau

1440cm
LCM of 48, 72 is 144cm, i.e. for each 144cm there will be one footprint overlapped.
let      z=周長
no of footprint made by 小飛=z/48
no of footprint made by 爺爺=z/72
no of footprint overlapped = z/144
since total visible footprint=40
then , z/48+z/72-z/144=40
          (3z+2z-z)/144=40
                      4z/144=40
                               z=1440  

Unclejt

2 steps of Grandpa = 3 steps of Fei = 144厘米

Excluding the initial 腳印, there will be 4 腳印 for each 144厘米.

As there are altogether 40 腳印, the length is 144 *10厘米.

sausauma

Dear freddielau & unclejt

You are so great!

Many tks