The snapback timing method was used to obtain average times for work elements in one work cycle. The times are given in the table below. Element d is a machine controlled element and the time is constant. Elements a$,$ b$,$ c$,$ e$,$ and f are operator controlled and were performance rated at $85\%$; however, elements e and $f$ are performed during the machine controlled element $d.$ The machine allowance is zero $($no extra time is added to the machine cycle$),$ and the PFD allowance is $15\%.$ Determine $($a$)$ the normal time for the cycle and $($b$)$ the standard time for the cycle. If the worker works $7$ hours and $10$min during an $8-$hour shift, and his performance level is $125\%,$ how many pieces are completed?

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