First find the total time Ellen spends painting lilies: 5 minutes/lily * 17 lilies = <<5*17=85>>85 minutes
Then find the total time Ellen spends painting roses: 7 minutes/lily * 10 roses = <<7*10=70>>70 minutes
Then find the total time Ellen spends painting orchids: 3 minutes/orchid * 6 orchids = <<3*6=18>>18 minutes
Then find the total time Ellen spends painting vines: 2 minutes/lily * 20 vines = <<2*20=40>>40 minutes
Then add the amount of time Ellen spends on each type of flower to find the total time: 85 minutes + 70 minutes + 18 minutes + 40 minutes = <<85+70+18+40=213>>213 minutes
#### 213