Question 4603
To find a rate of work, break the problem down into something that can be compared relatively easily.  In this case, look at how much work Pat gets done each hour.

Pat = completes {{{1/12}}} of the work every hour
Mike's rate of work is not known so we can say
Mike= completes {{{1/x}}} of the work every hour.

Together they work at a rate of 1/5 of the work completed each hour, so:
{{{1/12 + 1/x = 1/5}}}

Find a common denominator:
{{{5x/60x+60/60x=12x/60x}}}

Now we can drop the denominator:
5x+60=12x
subtract 5x from both sides:
60=7x
divide both sides by 7:
60/7=x or x=8.57

so Mike's rate of work is {{{1/8.57}}}, so he could finish the job in 8.57 hours by himself.