Final answer:
To determine the total time required to complete the job, Sofia and Noga's work rates are calculated, and the time Noga works alone after Sofia leaves is added to their joint work time. The entire job takes 13 hours to complete.
Step-by-step explanation:
To find out how long Sofia and Noga took to finish the job together, we will need to calculate their rates of work and then determine how much work was completed after Sofia left. Sofia can finish the work in 10 hours, so her work rate is 1/10 of the job per hour. Noga's work rate is 1/15 of the job per hour.
Working together for 4 hours, they complete (1/10 + 1/15) × 4 of the job. Simplifying this gives us 2/15 + 4/15, which equals to 6/15 or 2/5 of the entire job.
Since 2/5 of the job is done, there is 3/5 of the job remaining. Noga, working alone, would take 15 hours to do the entire job, so to do 3/5 of it, she takes 3/5 × 15 hours, which equals 9 hours.
The total time taken to finish the job is the 4 hours they worked together plus the 9 hours Noga worked alone. Therefore, the job took a total of 4 hours + 9 hours = 13 hours to complete.