Question 230944
What you need to do is to add together 
their rates of working to get their rate
working together
In words:
Owner's rate = (all the cages)/(7 hours)
Assistant's rate = (all the cages)/(11 hours)
Let {{{x}}} = their time working together
Call all the cages cleaned 1 job, so
{{{1/7 + 1/11 = 1/x}}}
Multiply both sides by {{{77x}}}
{{{11x + 7x = 77}}}
{{{18x = 77}}}
{{{x = 4.278}}} hrs
It takes them 4 hrs 16 min and 40 sec working together
check:
{{{1/7 + 1/11 = 1/x}}}
{{{1/7 + 1/11 = 1/4.278}}}
{{{.14286 + .09091 = .233766}}}
{{{.233769 = .233766}}} close enough