Casey wants to paint her 10 toenails + 10 fingernails = <<10+10=20>>20 nails in total.
First she wants to do a base coat which takes 20 minutes to apply + 20 minutes to dry = <<20+20=40>>40 minutes total for the first coat.
It will take the same amount of time to do a coat of paint and let it dry and to do a coat of glitter and let it dry, 40 minutes x 3 different coats = <<40*3=120>>120 minutes total to paint her toenails and fingernails.
#### 120