andrew can paint the neighbor's house 3 times as fast as bailey. 

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Let bailey's time be 3x days/job ;then his rate is 1/3x job/day

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Andrew's time is x days/job ; andrew's rate is 1d/x job/day

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the year they worked together it took them 2 days.

Together time = 2 days/job ; together rate = 1/2 job/day

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how long would it take for each one to paint the house alone?

Equation:

rate + rate = together rate

1/3x + 1/x = 1/2

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Multiply thru by 6x to get:

2 + 6 = 3x

x = 8/3 days (time for andrew to do the job alone).

3x = 8 days (time for bailey to do the job alone).

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Cheers,

Techidse :)