TABLE $10\mathrm{.}2$ The Execution Mix for Five Programs on Two Systems and the Weighted Average of the Running Times

TABLE $10\mathrm{.}3$ The Weighted Average Running Times for System A Using a Revised Execution Mix

$1.$ Table $10\mathrm{.}2$ shows an execution mix and runtimes for two computers, System A and System C$.$ In this example System C is $\backslash (83\backslash \%\backslash )$ faster than System A$.$ Table $10\mathrm{.}3$ shows runtimes for System A with a different execution mix. Using the execution mix in Table $10\mathrm{.}3,$ calculate the percentage by which System C would be faster than System A$.$ Using the original statistics from Table $10\mathrm{.}2,$ by how much has the performance of System A degraded under the new execution mix?

$2.$ With regard to the performance data cited for programs $\backslash (\backslash$mathrm$\{$v$\},\backslash$mathrm$\{$w$\},\backslash$mathrm$\{$x$\},\backslash$mathrm$\{$y$\}\backslash ),$ and z in Section $10\mathrm{.}3,$ find the geometric means of the runtimes of the programs for System B and System C using

System A as the reference system. Verify that the ratios of the means ig consistent with the results obtained using the other two systems as reference systems.