SOLUTION: A, B, and C can do a piece of work in 10 days. A and B can do it in 12 days, A and C in 20 days. How many days would it take each to do the work alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A, B, and C can do a piece of work in 10 days. A and B can do it in 12 days, A and C in 20 days. How many days would it take each to do the work alone?      Log On


   

Question 636702: A, B, and C can do a piece of work in 10 days. A and B can do it in 12 days, A and C in 20 days. How many days would it take each to do the work alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let their rates of working in ( fraction of work finished ) / ( days to do it )
= +R%5BA%5D+, +R%5BB%5D, and R%5BC%5D
given:
(1) +R%5BA%5D+%2B+R%5BB%5D+%2B+R%5BC%5D+=+1%2F10+
(2) +R%5BA%5D+%2B+R%5BB%5D+=+1%2F12+
(3) +R%5BA%5D+%2B+R%5BC%5D+=+1%2F20+
-----------------------
(2) +R%5BB%5D+=+1%2F12+-+R%5BA%5D+
(3) +R%5BC%5D+=+1%2F20+-+R%5BA%5D+
and, by substitution,
(1) +R%5BA%5D+%2B+%28+1%2F12+-+R%5BA%5D+%29+%2B+%28+1%2F20+-+R%5BA%5D+%29+=+1%2F10+
(1) +1%2F12+%2B+1%2F20+-+R%5BA%5D+=+1%2F10+
(1) +R%5BA%5D+=+1%2F12+%2B+1%2F20+-+1%2F10+
{1) +R%5BA%5D+=+5%2F60+%2B+3%2F60+-+6%2F60+
(1) +R%5BA%5D+=+1%2F30+
-----------------
(2) +R%5BB%5D+=+1%2F12+-+R%5BA%5D+
(2) +R%5BB%5D+=+1%2F12+-+1%2F30+
(2) +R%5BB%5D+=+5%2F60+-+2%2F60+
(2) +R%5BB%5D+=+1%2F20+
----------------
(3) +R%5BC%5D+=+1%2F20+-+R%5BA%5D+
(3) +R%5BC%5D+=+1%2F20+-+1%2F30+
(3) +R%5BC%5D+=+3%2F60+-+2%2F60+
(3) +R%5BC%5D+=+1%2F60+
-----------------
A takes 30 days working alone
B takes 20 days working alone
C takes 60 days working alone
------------------------
check:
(1) +R%5BA%5D+%2B+R%5BB%5D+%2B+R%5BC%5D+=+1%2F10+
(1) +1%2F30+%2B+1%2F20+%2B+1%2F60+=+1%2F10+
(1) +2%2F60+%2B+3%2F60+%2B+1%2F60+=+6%2F60+
(1) +6%2F60+=+6%2F60+
OK