Answer:
I will suppose that 1/2 inches are lost in each connection.
If we have 7 pieces of duct, we have 5 connections (because the ones in the extremes are not connected)
Each piece of duct measures 48 inches, and in each connection, we lose 1/2 inches.
Then the equation here is:
Length = 7*48in - 5*1/2in = 333.5 inches.
If we have 12 pieces, then we have 12 - 2 = 10 connections (same situation as before) then the length will be
Length = 12*48in - 10*1/2in = 571 inches.