SOLUTION: One machine can turn out 1000 pieces in 12 days. A second machine takes 18 days to turn out 1000 pieces. On a particular run the first machine operated for 4 days alone. The second

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One machine can turn out 1000 pieces in 12 days. A second machine takes 18 days to turn out 1000 pieces. On a particular run the first machine operated for 4 days alone. The second      Log On


   

Question 414561: One machine can turn out 1000 pieces in 12 days. A second machine takes 18 days to turn out 1000 pieces. On a particular run the first machine operated for 4 days alone. The second machine was then put into operation, and the two worked together. How long did it take to finish 1000 pieces
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
One machine can turn out 1000 pieces in 12 days.
A second machine takes 18 days to turn out 1000 pieces.
On a particular run the first machine operated for 4 days alone.
The second machine was then put into operation, and the two worked together.
How long did it take to finish 1000 pieces?
:
Let t = time that the two machines worked together
:
Let the completed job = 1 (1000 pieces made)
:
Mach 1 + Mach 2
%28t%2B4%29%2F12 + t%2F18 = 1
Multiply eq by 26 to clear the denominators, results:
3(t+4) + 2t = 36
:
3t + 12 + 2t = 36
5t = 36 - 12
5t = 24
t = 24%2F5
t = 4.8 days working together to finish the job
:
:
Check this: (Machine 1 worked 8.8 days)
8.8/12 + 4.8/18 =
.733 + .267 = 1.0 confirms our solution of 4.8 days working together