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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 :))

 #1
avatar+214 
+2

Hope someone will helpsmiley.

edited by aboslutelydestroying  Apr 4, 2024
 #2
avatar+128794 
+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

 

cool cool cool

 Apr 5, 2024
 #3
avatar+15 
+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
 #4
avatar+128794 
+1

OK...i'll try to think about it a litle more

 

cool cool cool

CPhill  Apr 5, 2024

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