Problem $5(30$ points$)$: A speed$-$reducer gearbox containing a compound reverted gear train transmits $35$ horsepower with an input speed of $1200$ rev$/$min$.$ Spur gears with $20$o pressure angle are used, with $16$ teeth on each of the small gears and $48$ teeth on each of the larger gears. A diametral pitch of $10$ teeth$/$in is proposed. $($a$)$ Determine the speeds of the intermediate and output shafts. $($b$)$ Determine the pitch line velocities $($in ft$/$min$)$ for each set of gears. $($c$)$ Determine the magnitudes of the tangential$,$ radial, and total forces transmitted between each set of gears. $($d$)$ Determine the input torque. $($e$)$ Determine the output torque, neglecting frictional losses.