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