$13\mathrm{.}9$ The continuous timing method in direct time study was used to obtain the element times for a worker$-$machine task as indicated in the table below. Element $c$ is a machine$-$controlled element and the time is constant. Elements $a,b,d,e,$ and $f$ are operator$-$controlled and external to the machine cycle, and they were performance rated at $80\%.$ If the machine allowance is $25\%,$ and the worker PFD allowance is $15\%,$ determine $($a$)$ the normal time. $($b$)$ the standard time for the cycle, and $($c$)$ the worker's efficiency if the worker completes $360$ work units working $7\mathrm{.}2hr$ on an $8-$hour shift.

$\backslash$table$[[$Element$,a,b,c,d,e,f$