SOLUTION: 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work ?

Algebra ->  Proportions -> SOLUTION: 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work ?      Log On


   

Question 1088380: 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5B1%5D+ = the rate that men work
Let +R%5B2%5D+ = the rate that women work
( The rates are in [ work completed ] / [ days to complete the work ] )
---------------------------------------
(1) +3R%5B1%5D+%2B+7R%5B2%5D+=+1%2F10+
(2) +4R%5B1%5D+%2B+6R%5B2%5D+=+1%2F8+
-------------------------------
Multiply both sides of (1) by +4+ and
both sides of (2) by +3+
Then subtract (2) from (1)
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(1) +12R%5B1%5D+%2B+28R%5B2%5D+=+2%2F5+
(2) +-12R%5B1%5D+-+18R%5B2%5D+=+-3%2F8+
------------------------------------
(1) +12R%5B1%5D+%2B+28R%5B2%5D+=+16%2F40+
(2) +-12R%5B1%5D+-+18R%5B2%5D+=+-15%2F40+
------------------------------------
+10R%5B2%5D+=+1%2F40+
Ten women take 40 days to complete the work
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+R%5B2%5D+=+1%2F400+
check answer:
(1) +3R%5B1%5D+%2B+7R%5B2%5D+=+1%2F10+
(1) +3R%5B1%5D+%2B+7%2A%281%2F400%29+=+1%2F10+
(1) +1200R%5B1%5D+%2B+7+=+40+
(1) +1200R%5B1%5D+=+33+
(1) +R%5B1%5D+=+33%2F1200+
(1) +R%5B1%5D+=+11%2F400+
-------------------------
(2) +4R%5B1%5D+%2B+6R%5B2%5D+=+1%2F8+
(2) +4R%5B1%5D+%2B+6%2A%281%2F400%29+=+1%2F8+
(2) +1600R%5B1%5D+%2B+6+=+50+
(2) +1600R%5B1%5D+=+44+
(2) +R%5B1%5D+=+44%2F1600+
(2) +R%5B1%5D+=+11%2F400+
OK
Check the math & get a 2nd opinion if needed