Question 768485
Uniform Rates job-completion problem,
Let x = time for Shane to do one job; his rate is 1/x jobs per hour.
Then 2+x = time in hours for Brian to do the same job; which is 1/(x+2) job per hour.

THEY work together for 5 hours.
Let h = 5 hours.


Note, the description of the problem implied that Brian and Shane worked together and did ONE job.


Use the fundamental concept of rate.  
(jobs/time)=(jobs)/(time)
{{{r=j/t}}}__________ r is rate, j is amount of jobs, t is time.


USE THE FUNDAMENTAL CONCEPT OF UNIFORM RATE:
{{{highlight((1/x+1/(x+2))*h=1)}}}
That IS {rate}*{time}={job}.  Their rates are additive while they work together.  They do ONE job, shown as 1.


SYMBOLIC SOLUTION PROCESS:
Just substitute 5 for h, and solve the equation for x.  Tell if you have trouble with doing this.  Most of the analyzing and solution process is to obtain the equation highlighted.