Planets in orbit

[Frank23]

Two planets in orbit around a stationary star, each moving clockwise.The outer planet takes 60 years to complete an orbit, the inner planet 24 years. In how many years will the two planets next form a straight line with each other and the star? I left school a long time ago, so can anyone help me with this? In simple terms, not complicated equations as the last few remaining brain cells wont be able to cope.

[coinman]

i think the answer is 20 years

the inner planet rotates 15 degrees every year while the outer planet moves 6 degrees each year

after 20 years the inner planet moves 300 degrees and the outer planet moves 120 degrees so they will be in line but opposite each other

[Frank23]

Thank you, it seems so easy when you explain it like that.

[mohill]

Hi Frank23!

Just to add a note to coinman's excellent solution .... if at the start the two planets are on opposite sides of the star then the same time of 20 years will find them aligned once again but now they are on the same side of the star. What an interesting problem.

Cheers