If Jackie were to paint her living room alone it would take five hours. Her sister Violet could do the job in six hours. How long would it take them working together?

Find how much work they get done in 1 hour

jackie takes 5 hours to do 1 room, so in 1 hour, she does 1/5 room

voilet take 6 hours to do 1 room so in 1 hour, she does 1/6 room

together, they do 1/5+1/6 room in 1 hour

make common denom

1/5+1/6=6/30+5/30=11/30 in 1 hour

11/30 times time=1 room

times both sides by 30/11

time=30/11 hour

time=2 and 8/11 hour

that is about 2 hours and 44 mins

2 and 8/11 hour or 30/11 hours