SOLUTION: three machines A , B and C take 3 hours to do a job, when working together. Suppose A and B are identical and that C working alone can complete the entire job in 12 hrs. How long w

Algebra ->  Rate-of-work-word-problems -> SOLUTION: three machines A , B and C take 3 hours to do a job, when working together. Suppose A and B are identical and that C working alone can complete the entire job in 12 hrs. How long w      Log On


   

Question 234049: three machines A , B and C take 3 hours to do a job, when working together. Suppose A and B are identical and that C working alone can complete the entire job in 12 hrs. How long would it take A working alone to do the job?
a)4 hrs b) 8 hrs c)10 hrs d)12 hrs e) None of these
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
three machines A , B and C take 3 hours to do a job, when working together.
Suppose A and B are identical and that C working alone can complete the entire job in 12 hrs.
How long would it take A working alone to do the job?
:
Let t = time for A or B working alone (Identical machines)
:
Let the completed job = 1
:
3%2Ft + 3%2Ft + 3%2F12 = 1
:
6%2Ft + 3%2F12 = 1
Multiply equation by 12t, results
12(6) + 3t = 12t
:
72 = 12t - 3t
:
72 = 9t
t = 72%2F9
t = 8 hrs, A working alone
;
:
Check solution
3%2F8 + 3%2F8 + 3%2F12 =
6%2F8 + 1%2F4 = 1