gbq 50

[theskin]

so frustrated with this(not very good at things mathematical)

Two planets orbit a star.starting in a line.outer planet takes 60 years to make a complete orbit while the inner takes 24 years.how many years before the three objects next form a straight line?

any clue would be much appreciated.thanks.

[crofter]

theskin You say that you want a clue rather than the solution - and I respect that! Firstly you need to appreciate that there are several ways they could form a straight line. Namely:

Planet A------------STAR----------------------Planet B

STAR----------------Planet A-------------Planet B

It does not matter which case you assume, but you will find the problem easier if you stick with it when you "next next form a straight line"!

Once this is agreed then you begin to think along the lines of the LCM = Lowest Common Multiple of 24 and 60! Good Luck!

[Andy Cheever]

Crofter, your reasoning of the LCM is not right. The LCM of 24 and 60 is 120, which is way beyond the actual answer. I think a better clue for theskin is that if the inner planet takes 24 years to complete a FULL orbit - does it form a straight line with the outer planet in that 24 year period?

AC

[theskin]

thank you both.i have the answer now.

[crofter]

Apologies to theskin and thanks to Andy, I was being a bit too rash! It will take 120 years before they both return to their starting positions.

Every 20 years the two planets will switch from the upper pattern to the lower patter (and back again) as shown in my original posting.

In fact, the outer planet is sweeping through 6 degrees per year and the inner planet 15 degrees per year. In T years, they will sweep through angles of 6T and 15T. All three bodies are collinear again, if

6T + 180 = 15T which leads to T = 20

I hope juliefer doesn't see this!