SOLUTION: A,B and C 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?

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Question 745478: A,B and C 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 savvyhush23(50) About Me  (Show Source):
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A,B and C 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?
Let x,y and z be the rate,
A,B and C do a piece of work in ...x%2By%2Bz=1%2F10
A and B can do it in 12 days...x%2By=1%2F12
A and C in 20 days...x%2Bz=1%2F20
Solving simultaneous equation yields,
x=1%2F30,y=1%2F20,z=1%2F60
How many days would it take each to do the work alone?
Time=Work%2FRate
A=1%2Fx=30+days
B=1%2Fy=20+days
C=1%2Fz=60+days