SOLUTION: jim's copier can do a printing job in 7 hours. janet's copies can do the same job in 12 hours. how long would it take to do the job with both copies?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: jim's copier can do a printing job in 7 hours. janet's copies can do the same job in 12 hours. how long would it take to do the job with both copies?      Log On


   

Question 889347: jim's copier can do a printing job in 7 hours. janet's copies can do the same job in 12 hours. how long would it take to do the job with both copies?
Found 2 solutions by josmiceli, LinnW:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of printing
Jim's:
( 1 job ) / ( 7 hrs )
Janet's:
( 1 job ) / ( 12 hrs )
-------------------
Let +t+ = time in hours for
both printers to do the job
+1%2F7+%2B+1%2F12+=+1%2Ft+
Multiply both sides by +7%2A12%2At+
+12t+%2B+7t+=+7%2A12+
+19t+=+84+
+t+=+84%2F19+
+t+=+4+%2B+8%2F19+
+%28+8%2F19+%29%2A60+=+25.26+
+.26%2A60+=+16+
-----------------------
It will take both copiers 4 hrs 25 min 16 sec
check answer:
+1%2F7+%2B+1%2F12+=+1%2Ft+
+1%2F7+%2B+1%2F12+=+1%2F%2884%2F19%29+
+1%2F7+%2B+1%2F12+=+19%2F84+
+12%2F84+%2B+7%2F84+=+19%2F84+
+19%2F84+=+19%2F84+

Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Jims copier does 1/7 of a job per hour
Janets does 1/12 per hour
Set t = time to complete a job
t(1/7) + t(1/12) = 1 job
t(1/7 + 1/12) = 1
use 7*12 as a common denominator

t+%28+12%2F%2812%2A7%29+%2B+7%2F%2812%2A7%29+%29+=+1+
t+%28+19%2F84+%29+=+1+
multiply each side by 84%2F19
t = 84%2F19 = 4.421 hours