Patrice, by himself, can paint four rooms in 10 hours. if he hires april to , they can do the same job together in 6 hours. if he lets april work alone, how long will it take her to paint the four rooms?

-- The whole discussion involves 4 rooms, never more and never less,
so we can call the 4 rooms "1 job" for simplicity.

-- Patrice, by himself, does the job in 10 hours.  So he does 1/10 of
the job each hour.

-- Working together, Patrice and April do the job in 6 hours.  So when
they work together, they do 1/6 of the job each hour.

-- April's part of the job is (1/6 - 1/10) = (5/30 - 3/30) = 2/30 = 1/15 job per hour.

-- Her unit rate alone is  1/15 job per hour, or  15 hours per job.