In a production turning operation, the work part diameter $=102$mm $$and length $=400$mm $$long$.$ A feed of $0\mathrm{.}26$ mm$/$rev $$is used in the operation. If cutting speed $=3\mathrm{.}0$m$/$s$,$the tool must be changed every $5$work parts; but if cutting speed $=2\mathrm{.}0$m$/$s$,$the tool can be used to produce $22$pieces between tool changes. Determine the Taylor Tool Life equation for this job.