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Jane Street

There is a solar system with three planets orbiting around the sun. One of them has a translation period of 60 years, another one of 84 years and another one of 140 years. Today, the three planets are aligned with the sun. When is the next time the three planets will be aligned with the sun?

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10 respuestas

14

Should be 210 years

Answer en

1

These planets can be aligned on either the same side of the sun or opposite sides. So the answer is a number x that is the least common multiplier of 30, 42 and 70, which is 210.

Jimmy en

0

sorry i was wrong

summer zheng en

0

1/(1/60-1/84)=84*60/24=210, 1/(1/60-1/140)=140*60/80=210/2, so 210 years...

Anónimo en

0

t (in years): next time for the 3 planets align with sun t/60 - t/84 = 0.5*a t/60-t/140 = 0.5*b a and b are positive integers. Minimum t satisfied the equations above will be the answer.

ky en

0

ky's answer is right. Solve the equations you can get t=105k, where k is a positive integer. If you are not convinced, you can check that after 105 years the three planets are indeed aligned with the sun.

Fang the Spectator en

0

AB will meet every 60 years BC will meet every 210 years ABC will meet every 420 years

summer zheng en

0

any multiples of 105/2 years such as 105/2, 105, 105*3/2...

summer zheng en

3

4x3x5x7=420

Anónimo en

0

105 works too

Anónimo en

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