Sally can paint a room in 3 hours while it takes Steve 5 hours to paint the same room. How many hours will it take them to paint the room if they worked together?
Sally can paint at a rate of 1 room per 3 hours, or `1/3` room per hour. Steve can paint at a rate of 1 room per 5 hours, or `1/5` room per hour. Together, they paint at the rate of `1/3+1/5=5/15+3/15=8/15` room per hour. So they can paint one room in `15/8` hours. The formula for this in terms of their original rates `r_1,r_2` is
`1/(r_1+r_2),` which in this case, with `r_1=1/3` and `r_2=1/5,` does simplify