a girl can make a case of tie dye nail polish in two seconds, and another girl can make a case of tie dye nail polish in 3 seconds. If they work together how long will it take for them to make 10 cases of tie dye nail polish?
If one girl can make a case in 2 seconds and another girl can make a case in 3 seconds, their combined rate of work is 1/2 + 1/3 = 5/6 cases per second.
It will take them 10 / (5/6) = (10 * 6) / 5 = <<10*(6/5)=12>>12 seconds to make 10 cases together. Answer: \boxed{12}.