Four people can paint a house in six hours. How many hours would it take three people to paint the same house, assuming everyone works at the same rate?
To solve this problem, I need to find the relationship between the number of people, the time, and the amount of work done. I can use the concept of rate of work, which is the amount of work done per unit of time. If four people can paint a house in six hours, then their combined rate of work is 1/6 of a house per hour. That means each person's individual rate of work is 1/24 of a house per hour, since they all work at the same rate. Now I can use this rate to find out how long it would take three people to paint the same house. If three people work together, their combined rate of work is 3/24 or 1/8 of a house per hour. That means they can paint the whole house in 8 hours, since 8 times 1/8 is 1. Therefore, the answer is 8 hours. 