One partner can paint the Edison Mansion 5 days. His competitor can do the job in 6 days. If they agreed to work together at the same time and didn't interfere with each other, how long would it take them if they work at their normal rate of speed?

2.73 days, working together without interference

Step-by-step explanation:

The following formulas are pertinent here:  1 job = (rate)(time) and

                  1 job

time =

              1 job / days

In this specific case, there are two rates:  1 job / 5 days and 1 job / 6 days.

The combined rate would be:

1 job          1 job            6 + 5

+ = = 11/30 job/day

5 days      6 days         (6)(5)

and so we have:

                1 job

time = = 30/11 days, or 2.73 days

            (11/30)(job/day)