SOLUTION: A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes in 13 days. In

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes in 13 days. In       Log On


   

Question 934977: A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes in 13 days. In how many days C alone will do the work?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a= fraction of the job A can do in 1 day.
b= fraction of the job B can do in 1 day.
c= fraction of the job C can do in 1 day.

"A and B together can do a piece of work in 12 days" translates as
12%28a%2Bb%29=1<--->12a%2B12b=1<--->a%2Bb=1%2F12 .
Since that is a job "which B and C together can do in 16 days" ,
16%28b%2Bc%29=1<--->16b%2B16c=1<--->b%2Bc=1%2F16 .
"After A has been working at it for 5 days and B for 7 days, C finishes in 13 days" translates as
5a%2B7b%2B13c=1 .
You get the system
system%28a%2Bb=1%2F12%2Cb%2Bc=1%2F16%2C5a%2B7b%2B13c=1%29 <---> system%28-5a-5b=-5%2F12%2C-2b-2c=-1%2F8%2C5a%2B7b%2B13c=1%29 .
If you add all 3 equations, you get
13c-2c=1-5%2F12-1%2F8--->11c=24%2F24-10%2F24-3%2F24--->11c=11%2F24--->c=1%2F24 .
Since C can do 1%2F24 of the joy each day,
C alone will do the work in highlight%2824+days%29 .