SOLUTION: working alone,photography machine C requires 40 minutes to complete an 800 page job.working together machines B and C require 25 mins for the same 800 page job.with machines A,B an

Algebra ->  Rate-of-work-word-problems -> SOLUTION: working alone,photography machine C requires 40 minutes to complete an 800 page job.working together machines B and C require 25 mins for the same 800 page job.with machines A,B an      Log On


   

Question 1045439: working alone,photography machine C requires 40 minutes to complete an 800 page job.working together machines B and C require 25 mins for the same 800 page job.with machines A,B and C working together, the job takes 10 minutes. how long does it take machine A to complete the Job working alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r%5BA%5D+ = the rate of working for
machine A in pages/min
Let +r%5BB%5D+ = the rate of working for
machine B in pages/min
Let +r%5BC%5D+ = the rate of working for
machine C in pages/min
--------------------------------
(1) +r%5BC%5D+=+800%2F40+
(1) +r%5BC%5D+=+20+
and
(2) +r%5BB%5D+%2B+r%5BC%5D+=+800%2F25+
(2) +r%5BB%5D+%2B+r%5BC%5D+=+32+
and
(3) +r%5BA%5D+%2B+r%5BB%5D+%2B+r%5BC%5D+=+800%2F10+
(3) +r%5BA%5D+%2B+r%5BB%5D+%2B+r%5BC%5D+=+80+
-------------------------------
(2) +r%5BB%5D+%2B+r%5BC%5D+=+32+
(2) +r%5BB%5D+%2B+20+=+32+
(2) +r%5BB%5D+=+12+
and
(3) +r%5BA%5D+%2B+r%5BB%5D+%2B+r%5BC%5D+=+80+
(3) +r%5BA%5D+%2B+12+%2B+20+=+80+
(3) +r%5BA%5D+=+48+
--------------------------------
The rate of working of macine A is +48+ pages/min
Let +t+ = time in min for A to finish +800+ pages
+48%2F1+=+800%2Ft+
+t+=+800%2F48+
+t+=+16+%2B+2%2F3+
convert +2%2F3+ min to sec
+%282%2F3%29%2A60+=+40+
--------------------
Machine A takes 16 min 40 sec to do 800 page job
--------------------
check answer:
(3) +r%5BA%5D+%2B+r%5BB%5D+%2B+r%5BC%5D+=+80+
(3) +800%2F16.667+%2B+12+%2B+20+=+80+
(3) +48+%2B+12+%2B+20+=+80+
(3) +80+=+80+
Hope I got it!