SOLUTION: One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one ma

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one ma      Log On


   

Question 927618: One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them four hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5Bw%5D+ = rate of working for a woman in jobs / hr
Let +R%5Bm%5D+ = rate of working for a man in jobs / hr
Let +R%5Bg%5D+ = rate of working for a girl in jobs / hr
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Add rates of working to get rate working together ( generally )
(3) +R%5Bm%5D+=+1%2F4+-+R%5Bg%5D+
(2) +R%5Bw%5D+%2B+2R%5Bg%5D+=+1%2F2+
(3) +R%5Bm%5D+%2B+R%5Bg%5D+=+1%2F4+
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This is 3 equations and 3 unknowns, so it's solvable
(3) +R%5Bm%5D+=+1%2F4+-+R%5Bg%5D+
Substitute this into (1)
(1) +1%2F4+-+R%5Bg%5D+%2B+R%5Bw%5D+=+1%2F2+
(1) +R%5Bw%5D+-+R%5Bg%5D+=+1%2F4+
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Subtract (1) from (2)
(3) +R%5Bm%5D+=+1%2F4+-+R%5Bg%5D+
(1) +-R%5Bw%5D+%2B+R%5Bg%5D+=+-1%2F4+
-------------------------
+3R%5Bg%5D+=+1%2F4+
+R%5Bg%5D+=+1%2F12+
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and, since:
(3) +R%5Bm%5D+=+1%2F4+-+R%5Bg%5D+
(3) +R%5Bm%5D+=+1%2F4+-+1%2F12+
(3) +R%5Bm%5D+=+3%2F12+-+1%2F12+
(3) +R%5Bm%5D+=+1%2F6+
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(1) +R%5Bw%5D+-+R%5Bg%5D+=+1%2F4+
(1) +R%5Bw%5D+-+1%2F12+=+1%2F4+
(1) +R%5Bw%5D+=+3%2F12+%2B+1%2F12+
(1) +R%5Bw%5D+=+1%2F3+
---------------------------
1 woman takes 3 hrs
1 man takes 6 hrs
1 girl takes 12 hrs
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check:
(3) +R%5Bm%5D+=+1%2F4+-+R%5Bg%5D+
(3) +1%2F6+=+1%2F4+-+1%2F12+
(3) +2%2F12+=+3%2F12+-+1%2F12+
(3) +2%2F12+=+2%2F12+
---------------------
(2) +R%5Bw%5D+%2B+2R%5Bg%5D+=+1%2F2+
(2) +1%2F3+%2B+2%2A%281%2F12%29+=+1%2F2+
(2) +4%2F12+%2B+2%2F12+=+6%2F12+
(2) +6%2F12+=+6%2F12+
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You can check the other one