SOLUTION: A can do a work in 36 days, B can do the work in 72 days and C can do the work in 78 days. The three take turns in working, i.e. A works on the first day, B works on the second day

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A can do a work in 36 days, B can do the work in 72 days and C can do the work in 78 days. The three take turns in working, i.e. A works on the first day, B works on the second day      Log On


   

Question 490214: A can do a work in 36 days, B can do the work in 72 days and C can do the work in 78 days. The three take turns in working, i.e. A works on the first day, B works on the second day, C on the third day and so on. Which day will they finish the work?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A can do a work in 36 days, B can do the work in 72 days and C can do the work in 78 days.
The three take turns in working, i.e. A works on the first day, B works on the second day, C on the third day and so on.
Which day will they finish the work?
:
Let d = the no. of days for the three men to do the work
Let the completed job = 1
:
%28%281%2F3%29d%29%2F36 + %28%281%2F3%29d%29%2F72 + %28%281%2F3%29d%29%2F78 = 1
Multiply by 2808 to clear the denominators
78(1%2F3d) + 39(1%2F3d) + 36(1%2F3d) = 2808
26d + 13d + 12d = 2808
51d = 2808
d = 2808%2F51
d = 55.06, therefore completion will occur on the 56th day