Andrew can paint the neighbor's house 3 times as fast as Bailey. The year Andrew and Bailey worked together, it took them 4 days. How long would it take each to paint the house?

Question

anonymous · Answer

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).

anonymous · Answer

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

anonymous · Answer

So would that make Andrew able to complete the house in 2 days and Bailey in 8?

mertsj · Answer

a = days it takes Andrew to paint the house
3a = days it takes Bailey to paint the house
1/a = part Andrew does in one day
1/3a = part Bailey does in one day.
1/4 = part they do together in 1 day.
$$\frac{1}{a}+\frac{1}{3a}=\frac{1}{4}$$
$$12+4=3a$$
$$a=\frac{16}{3}$$