Suppose that n machines A1, A2, ..., An produce the same product in the time span T

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^{Suppose that n machines A1, A2, ..., An produce the same product in the time span T and that the production times per unit are respectively t1, t2, ...tn Show that if all the machines had been equally efficient and together had produced exactly the same total amount in the time span t, then each machine's production time per unit would have been precisely the harmonic mean Th of t1, t2, ..., tn.}