SOLUTION: If 4 men and 6 boys can finish a piece of work in 24 days, in what time will 8 men and 9 boys finish it supposing that 8men can do as much work in 16 hours as 24boys can do in 12ho

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If 4 men and 6 boys can finish a piece of work in 24 days, in what time will 8 men and 9 boys finish it supposing that 8men can do as much work in 16 hours as 24boys can do in 12ho      Log On


   

Question 774674: If 4 men and 6 boys can finish a piece of work in 24 days, in what time will 8 men and 9 boys finish it supposing that 8men can do as much work in 16 hours as 24boys can do in 12hours?
A.12 days B.13 1/3 days C.15 days D.12 1/2 days
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If 4 men and 6 boys can finish a piece of work in 24 days,
Find the number of men and boy days to complete the work
24(4m) + 24(6b) = (96m + 144b)
:
in what time will 8 men and 9 boys finish it supposing that
:
8 men can do as much work in 16 hours as 24 boys can do in 12 hrs?
16(8m) = 12(24b)
128m = 288b
simplify, divide both sides by 32
4m = 9b
m = 9%2F4b
m = 2.25b
:
(96m + 144b) = the completed job
replace m with 2.25b
96(2.25b) + 144b =
216b + 144b = 360 boy-days to complete the job
:
"in what time will 8 men and 9 boys finish it
let t = number of days to do the job
8t + 9t = completed job
Change 8 men to boys: 8*2.25 = 18
18t + 9t = 360
27t = 360
t = 360/27
t = 13.33 days for 8 men and 9 boys to do the job