How long will it take them if they work together?

Question

Joe and jan want to clean their yard. Joe could do the job in 45 minutes working alone. Jan, working alone, could pick it up in 30 minutes. How long will it take them if they work together?

Answer 1

Let's imagine the yard contains 90 items to be cleared. Since Joe takes 45 minutes to remove the 90 items to clear the yard, he's working at the rate of 1/2 (45/90) minute to remove one item, or 2 items (90/45) every minute. Jan would remove 90 items in 30 minutes, so that's 3 items (90/30) a minute or one item in 1/3 minute (30/90).

If they work together, in one minute they could remove 5 items (2+3). To remove 90 items it would take 90/5=18 times as long=18 minutes to do the job.