The ratio of the lengths of orange to purple to grey is 1 : 3 : 1.
To find the ratio of the lengths of orange to purple to grey, you need to divide the lengths of each color by the smallest length. In this case, the smallest length is 0.6m, which is the length of the orange section. So, the ratio is:
Orange : Purple : Grey = 0.6 : 1.8 : 0.8
Now, simplify the ratio by dividing each length by 0.6:
Orange : Purple : Grey = 1 : 3 : 1.33
Since we need to use whole numbers only, approximate 1.33 as 1. Therefore, the simplest form of the ratio is:
Orange : Purple : Grey = 1 : 3 : 1