SOLUTION: aron, Brenda, Charlie, and Danita are house painters. The team of Aaron, Brenda, and Charlie can paint my house in 3 days; if Aaron and Danita work as a pair it takes 6 days; the p

Algebra ->  Rate-of-work-word-problems -> SOLUTION: aron, Brenda, Charlie, and Danita are house painters. The team of Aaron, Brenda, and Charlie can paint my house in 3 days; if Aaron and Danita work as a pair it takes 6 days; the p      Log On


   

Question 722406: aron, Brenda, Charlie, and Danita are house painters. The team of Aaron, Brenda, and Charlie can paint my house in 3 days; if Aaron and Danita work as a pair it takes 6 days; the pair of Charlie and Danita takes 8 days, and the team of Brenda, Charlie, and Danit can finish in 5 days. How long would it take the whole 4-person crew to paint my house?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r%5Ba%5D+ = Aaron's rate of painting in houses/day
Let +r%5Bb%5D+ = Brenda's rate of painting in houses/day
Let +r%5Bc%5D+ = Charlie's rate of painting in houses/day
Let +r%5Bd%5D+ = Danita's rate of painting in houses/day
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Add rates to get the rate working together
(1) +r%5Ba%5D+%2B+r%5Bb%5D+%2B+r%5Bc%5D+=+1%2F3+
(2) +r%5Ba%5D+%2B+r%5Bd%5D+=+1%2F6+
(3) +r%5Bc%5D+%2B+r%5Bd%5D+=+1%2F8+
(4) +r%5Bb%5D+%2B+r%5Bc%5D+%2B+r%5Bd%5D+=+1%2F5+
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This is 4 equations and 4 unknowns, so it should be solvable
Subtract (4) from (1)
(1) +r%5Ba%5D+%2B+r%5Bb%5D+%2B+r%5Bc%5D+=+1%2F3+
(4) +-r%5Bd%5D+-+r%5Bb%5D+-+r%5Bc%5D+=+-1%2F5+
(4) +r%5Ba%5D+-+r%5Bd%5D+=+5%2F15+-+3%2F15+
(4) +r%5Ba%5D+-+r%5Bd%5D+=+2%2F15+
--------------------
Add this result to (2)
(2) +r%5Ba%5D+%2B+r%5Bd%5D+=+1%2F6+
(4) +r%5Ba%5D+-+r%5Bd%5D+=+2%2F15+
+2r%5Ba%5D+=+5%2F30+%2B+4%2F30+
+2r%5Ba%5D+=+1%2F30+
+r%5Ba%5D+=+1%2F60+
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and, since
(2) +r%5Ba%5D+%2B+r%5Bd%5D+=+1%2F6+
(2) +1%2F60+%2B+r%5Bd%5D+=+1%2F6+
(2) +r%5Bd%5D+=+10%2F60+-+1%2F60+
(2) +r%5Bd%5D+=+9%2F60+
(2) +r%5Bd%5D+=+3%2F20+
You can finish- have to go