A production line with four automatic workstations $($the other stations are manual$)$ produces a certain product whose total assembly work content time $=55\mathrm{.}0$min. of direct manual labor. The production rate on the line is $45$unit$\frac{s}{h}r.$ Because of the automated stations, efficiency $=89\%.$ The manual stations each have one worker. It is known that $10\%$ of the cycle time is lost due to repositioning. If the balancing efficiency $E_b=0\mathrm{.}92$ on the manual stations, find $(4$ decimal points$)$:

$($a$)$ cycle time

$($b$)$ number of workers

$($c$)$ workstations on the line