Question 126557
Machine 1:
1.  can fill 1000 cases of soda in 3 hours, therefore:
2.  can fill 5000 cases of soda in 15 hours 
3.  can perform 1/15 of this job in one hour 
Machine 2:
1. can fill 1000 cases of soda in 5 hours, therefore: 
2. can fill 5000 cases of soda in 25 hours
3. can perform 1/25 of this job in one hour 

In one hour the two machines working together can perform {{{1/15 + 1/25}}} or {{{5/75 + 3/75}}} or {{{(8/75)}}} of the job.


Let x = the number of hours required for Machine 1 and Machine 2 to fill 5000 cases.
The number of hours (x) multiplied by the part of the job completed in 1 hour {{{(8/75)}}} equals the total job completed (1 or 100%)
Set up the equation:
{{{x(1/15 + 1/25) = 1}}}
Find lowest common denominator: 
{{{x(5/75 + 3/75) = 1}}}
Add: 
{{{x(8/75) = 1}}}
Solve: 
{{{x = 75/8}}}
{{{x = 9.375}}}

Together the machines can perform this job in {{{9.375}}} hours or about 9 hours and 22 minutes.