Quick math puzzle

100gSoma

hey folks,

here it is. From Mensa magazine this month. Im interested to see the thought process in how you tackle it... Thanks

http://www.iolfree.ie/~gamesroom2000/puzzle.jpg

red_fox

Well assuming the the orbits are the same shape (so that when using the diagram the speed of the planets is proportional to each other at the same angle (algle to the verial starting position of the promblem, say)) Then they're going to be in line when at the same angle, which will happen when the differance the number of orbits is a whole number, here it would be (t=time)

t/70 - t/120 = t/168

so every 168years, I think...

Pherekydes

I'm going for 84 years.

Reasoning:

Planet A travels at 3 degrees per year.
Planet B travels at 5.14 degrees per year.

Their difference is 2.14 deg/yr.

At that stage they are 180 degrees apart (in line, but on opposite sides of the sun).

180/2.14 is 84.

Numbers have been rounded for convenience.

w66w66

84 I think

after half an orbits it’s 60 yrs for A, so that’s 12/12.

so 35 yrs for b to do half orbit so 7/12 . so after A has done half an orbit that would put b ahead by 5/12. after another quarter orbit from A that would put b ahead by 7.5/12. that’s 90 yrs, they where in line when b was at 7/12 ahead. so at half it was 60 and now it’s 90 so the 2.5 increase in b’s lead was 30 so .5 is 6 .90-6 =84

100gSoma

Slow coach wrote:

At that stage they are 180 degrees apart (in line, but on opposite sides of the sun).

180/2.14 is 84.

I like this idea of "in line but opposite sides of the sun". What is the answer if they need to be in line like the start? 110yrs or somewhere about there?
It must be more than 70 and less than 120 right?

w66w66

it'd probably be double so 168yr.

Pherekydes

100gSoma wrote:

I like this idea of "in line but opposite sides of the sun". What is the answer if they need to be in line like the start? 110yrs or somewhere about there?
It must be more than 70 and less than 120 right?

No, it's as the first guy said: 168 years.

Reasoning is the same as before:

Planet A travels at 3 deg/yr
Planet B travels at 5.14 deg/yr

Their difference is 2.14 deg/yr.

At the required stage, they are 360 degrees apart (360 = 0 mod 360, ).

360/2.14 is 168.

Tar.Aldarion

It would be 84, I imagine it is allowing them to meet in a straight line at any 'point'.

100gSoma

Slow coach wrote:

Planet A travels at 3 deg/yr
Planet B travels at 5.14 deg/yr

Their difference is 2.14 deg/yr.

360/2.14 is 168.
180/2.14 is 84.

Thats sweet slow coach. so you use 360 degrees to be in line as like the start or 180 degrees to form a "straigh line" with each other and the sun. Thanks for all the suggestions lads. Explains perfectly how to tackle such problems.

Hagar

The question is flawed.
Isn't a year the time it takes a planet to orbit it's sun?
So who's years are we using to measure the time elapsed? Planet A or Planet B?
Is the answer therefore 1/2 year of the planet who's "time" we are using to measure elapsed time?

100gSoma

Hagar wrote:

The question is flawed.
Isn't a year the time it takes a planet to orbit it's sun?
So who's years are we using to measure the time elapsed? Planet A or Planet B?
Is the answer therefore 1/2 year of the planet who's "time" we are using to measure elapsed time?

No need to double post. I answered your comments in After Hours...

a year is the time it takes "EARTH" to orbit "OUR" sun... This measurement is used throughout astronomy. For example, Jupiter takes 11.86 years(earth years) to orbit the sun.

I think your thinking on the question is a tad too complex there Hager. good one though.

Hagar

Sorry about the double post.