Final answer:
Calculating the combined work rate of two individuals working together (1/10 + 1/15 job/hour), they complete 2/3 of the job in 4 hours. When the first person leaves, 1/3 of the job remains, which the second person completes in 5 hours, totaling 9 hours to finish the job.
Step-by-step explanation:
When considering two individuals working together on a job, where the first person can complete the job in 10 hours and the second person takes 15 hours, we need to find their combined work rate and how long they work together to solve the problem. First, we determine each person's work rate. The first person's work rate is 1 job per 10 hours (1/10 job/hour), and the second person's work rate is 1 job per 15 hours (1/15 job/hour). Adding these rates gives us the combined rate when they work together.
The combined work rate is 1/10 job/hour + 1/15 job/hour, which simplifies to (3/30 + 2/30) job/hour or 1/6 job/hour. They work together for 4 hours, hence they complete 4 * (1/6) job, which is 2/3 of the job. This means that 1/3 of the job is left after they have worked together for 4 hours. The first person then leaves, and the second person continues to work on the remaining 1/3 of the job alone. Since the second person's work rate is 1/15 job/hour, it will take them 15 hours to finish one full job. To complete 1/3 of the job, it would take 1/3 of 15 hours, which is 5 hours. Therefore, the remaining time required for the second person to complete the job is 5 hours. In total, with both individuals working together and then one person completing the job, it will take 4 hours (together) + 5 hours (second person alone) for a total of 9 hours to complete the entire job.