SOLUTION: Two machines fill cereal boxes at the same rate. After the two machines work together for 7 h, one machine breaks down. The second machine requires 14 more hours to finish filling

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Question 885907: Two machines fill cereal boxes at the same rate. After the two machines work together for 7 h, one machine breaks down. The second machine requires 14 more hours to finish filling the boxes. How long would it have taken one of the machines, working alone, to fill the boxes?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
r = the rate of each machine in JOBS per HOUR.
The description and question imply that 1 job will be done with the two machines. The question asks for finding r.

RT=J rate, time, job

First seven hours, both machines.
%28r%2Br%29%2A7 = amount of job done after both machines.

Last fourteen hours, only one machine.
r%2A14 = amount of job done using only one machine.

The sum of those two amounts of job are 1 whole job.
2r%2A7%2Br%2A14=1
14r%2B14r=1
28r=1
highlight%28r=1%2F28%29-----ONE JOB IN 28 HOURS, the rate of one machine.