A piece of duct measures 48 inches. When pieces are fitted together, 1 2 inches is lost connecting each successive length of duct. On the job 7 and
12 pieces of ducting are used. What, in inches is the total length of the
finished duct?

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.

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