Work Word Problem

Question

If it would take Mark m hours to clean the house alone, and with his brother Sam they can clean the house in t hours. How many hours would have taken Sam if he was working alone?

Answer 1

Mark's rate is 1 task/m hours and for both Sam & Mark, the rate is 1 task/t hours

We don't know Sam's rate, so let's use x as his rate

Working together (Mark) 1 task/m hours + (Sam) 1 task/x hours = 1 task/t hours

This implies 1/m + 1/x = 1/t Solving for x = tm/(m-t) hours/task and we know t<m