Juan takes 15 hours to do a job that his father can do in 6 hours. if juan works for 4.5 hours before his father joins him, how long will it take the two of them working together to finish the job?

Work it exactly like the other one with Wilda and Karla.

Juan takes 15 hours to do a job ... he does 1/15 of it in an hour.
His father can do it in 6 hours ... he does 1/6 of it in an hour.

Juan works alone for 4.5 hours.  In that time, he does  4.5/15 = 0.3
of the job.  When his father joins him, there's only 0.7 of it to finish.

Working together, they do (1/15 + 1/6) = (2/30 + 5/30) = 7/30 of the job
each hour.

How many times do they have to do  7/30  of the job in order to finish
the  7/10  of it that remains ?  That will be the number of hours they need.

(7/10) / (7/30) = 7/10 x 30/7 = 3 hours.

Then they can knock off while it's still daylight, and go for a swim.