Question

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?

Answer 1

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.