In this part, assume that each person works at the same rate.
10 people can complete a job in 9 hours.
If 15 people work on the same job, how many hours will it take to complete the job?

This is a problem involving inverse proportion. When one quantity (number of people) increases, the other quantity (time taken) decreases, assuming the total amount of work remains constant. **Method 1: Total work method** 1. Calculate the total amount of work required for the job. We can measure this in "person-hours". Total work = (number of people) × (time taken) Total work = 10 people × 9 hours = 90 person-hours. 2. Now, we have 15 people doing the same 90 person-hours of work. We can find the new time. New time = Total work / New number of people New time = 90 person-hours / 15 people = 6 hours. **Method 2: Ratio method** 1. The number of people changes from 10 to 15. The scaling factor is 15/10 = 3/2. 2. Since it's inverse proportion, the time will change by the reciprocal of this factor, which is 2/3. 3. New time = Original time × (2/3) New time = 9 hours × (2/3) = (9 × 2) / 3 = 18 / 3 = 6 hours. Both methods show that it will take 6 hours for 15 people to complete the job.