When Luke takes the 70-minute bus to work, his coworker Paula takes 3/5*70 = <<70*3/5=42>>42 minutes to travel from home to work.
From work to home, Paula spends the same amount of time she spent going to work, giving a total of 42+42 = <<42+42=84>>84 minutes in a day traveling.
From work to home, while riding the bike, Luke spends 5*70 = <<5*70=350>>350 minutes on the road.
The total time Luke takes to travel from home to work and back is 350+70 = <<350+70=420>>420 minutes.
Together, Luke and Paula takes 420+84 = <<420+84=504>>504 minutes
#### 504