Question 883050
Uniform Rates for doing work or a task or a job:
RT=J   Rate, Time, Job.
The rate in this form is in amount of job per time.  The numerator of the rate is quantity of job and the denominator in the rate is quantity of time.  You also should understand that for a given agent doing some work, the ratio J/T is a constant, which is R for the agent.


Ronnie takes 4 hours longer than Tim to paint a room.
Let x = time needed for Tim to do the job.
Tim's rate is {{{1/x}}}.
Ronnie's rate is {{{1/(x+4)}}}.


if they work together they can paint the room in 9 hours.
Their combined rate is {{{1/9}}}.


The sum of their rates individually is the rate for the two working together or simultaneously:
{{{highlight(1/x+1/(x+4)=1/9)}}}.