Planets X, Y and Z take 360, 450 and 540 days, respectively, to rotate around the same sun. If the three planets are lined up in a ray having the sun as its endpoint, what is the minimum positive number of days before they are on the same line again? (Note: LCM of 360,450, and 540 is not the answer :))

aboslutelydestroying Apr 4, 2024

#2**+1 **

Here's what I get

Planet Y travels 360 / 450 = 4/5 as fast as Planet X

So.....Planet X has traveled 360° in 360 days

And Planet Y has traveled (4/5) * 360° = 288° in 360 days

So there is a 72° difference between them

So it takes 360 / 72 = 5 360 day periods before they are on the same line again

Planet Z travels 360 / 540 = 2/3 as fast as Planet X

Planet Z travels (2/3) 360 = 240° when Planet X travels 360°

So....there is a 120° difference between them

So...it takes 360 / 120 = 3 360 day periods before they are in the same line again

5 * 3 = 15 360 day periods = 5400 days

CPhill Apr 5, 2024

#3**+1 **

yeah i dont think thats right cuz i tried it and it said it was wrong

also it doesnt have to line up on the same line they started on

cheeeeeeese
Apr 5, 2024