SOLUTION: if 10 men and 15 women together can do a work in 6 days , 12 men and 27 women do the same work in 4 days , then find in how many days can 6 men and 11 women do the same work

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Question 891147: if 10 men and 15 women together can do a work in 6 days , 12 men and 27 women do the same work in 4 days , then find in how many days can 6 men and 11 women do the same work
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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if 10 men and 15 women together can do a work in 6 days ,
12 men and 27 women do the same work in 4 days ,
then find in how many days can 6 men and 11 women do the same work
:
let m = 1 man-day
let g = 1 girl-day
:
6(10) + 6(15) = 60m + 90g = completed job
also
4(12) + 4(27) = 48m + 108g = completed job
therefore
60m + 90g = 48m + 108g
60m - 48m = 108g - 90g
12m = 18g
m = 18%2F12g
m = 1.5g
:
Use the 1st equation to find how many girl-days to complete the job
Replace m with 1.5 g
60(1.5g) + 90g = 180g required to complete the job
:
" find in how many days can 6 men and 11 women do the same work"
let d = no. days required
6dm + 11dg = 180g
Replace m with 1.5g
6d(1.5g) + 11dg = 180g
9dg + 11dg = 180g
divide thru by g
9d + 11d = 180
20d = 180
d = 180/20
d = 9 days for 6 men and 11 girls to do the job
:
:
See if that checks out
9(6*1.5) + 9(11) =
9(9) + 99 =
81 + 99 = 180 girl-days a completed job